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Journal articles on the topic 'Quantal Response Equilibria'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Blavatskyy, Pavlo. "A Refinement of Logit Quantal Response Equilibrium." International Game Theory Review 20, no. 02 (June 2018): 1850004. http://dx.doi.org/10.1142/s0219198918500044.

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Unlike the Nash equilibrium, logit quantal response equilibrium is affected by positive affine transformations of players’ von Neumann–Morgenstern utility payoffs. This paper presents a modification of a logit quantal response equilibrium that makes this equilibrium solution concept invariant to arbitrary normalization of utility payoffs. Our proposed modification can be viewed as a refinement of logit quantal response equilibria: instead of obtaining a continuum of equilibria (for different positive affine transformations of utility function) we now obtain only one equilibrium for all possible positive affine transformations of utility function. We define our refinement for simultaneous-move noncooperative games in the normal form.

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2

Turocy, Theodore L. "Computing sequential equilibria using agent quantal response equilibria." Economic Theory 42, no. 1 (February 6, 2009): 255–69. http://dx.doi.org/10.1007/s00199-009-0443-3.

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3

Voliotis, Dimitrios. "Strategic market games quantal response equilibria." Economic Theory 27, no. 2 (February 2006): 475–82. http://dx.doi.org/10.1007/s00199-004-0594-1.

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4

Golman, Russell. "Quantal response equilibria with heterogeneous agents." Journal of Economic Theory 146, no. 5 (September 2011): 2013–28. http://dx.doi.org/10.1016/j.jet.2011.06.007.

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5

McKelvey, Richard D., and Thomas R. Palfrey. "Quantal Response Equilibria for Normal Form Games." Games and Economic Behavior 10, no. 1 (July 1995): 6–38. http://dx.doi.org/10.1006/game.1995.1023.

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6

Goerg, Sebastian J., Abdolkarim Sadrieh, and Tibor Neugebauer. "Impulse Response Dynamics in Weakest Link Games." German Economic Review 17, no. 3 (August 1, 2016): 284–97. http://dx.doi.org/10.1111/geer.12100.

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Abstract In a recent paper, Croson et al. (2015) experimentally study three weakest link games with multiple symmetric equilibria. They demonstrate that static concepts based on the Nash equilibrium (including multiple Nash equilibria, quantal response equilibria, and equilibrium selection by risk and payoff dominance) cannot successfully capture the observed treatment differences. Using Reinhard Selten’s impulse response dynamics, we derive a proposition that provides a theoretical ranking of contribution levels in the weakest link games. We show that the predicted ranking of treatment outcomes is fully consistent with the observed data. In addition, we demonstrate that the impulse response dynamics perform well in tracking average contributions over time. We conclude that Reinhard Selten’s impulse response dynamics provide an extremely valuable behavioral approach that is not only capable of resolving the indecisiveness of static approaches in games with many equilibria, but that can also be used to track the development of choices over time in games with repeated interaction.

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7

Friedman, Evan. "Stochastic Equilibria: Noise in Actions or Beliefs?" American Economic Journal: Microeconomics 14, no. 1 (February 1, 2022): 94–142. http://dx.doi.org/10.1257/mic.20190013.

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We introduce noisy belief equilibrium (NBE) for normal-form games in which players best respond to noisy belief realizations. Axioms restrict belief distributions to be unbiased with respect to and responsive to changes in the opponents’ behavior. The axioms impose testable restrictions both within and across games, and we compare these restrictions to those of regular quantal response equilibrium (QRE) in which axioms are placed on the quantal response function as the primitive. NBE can generate similar predictions as QRE in several classes of games. Unlike QRE, NBE is a refinement of rationalizability and invariant to affine transformations of payoffs. (JEL C72, D83, D91)

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8

Wolpert, David H. "Trembling hand perfection for mixed quantal/best response equilibria." International Journal of Game Theory 38, no. 4 (July 28, 2009): 539–51. http://dx.doi.org/10.1007/s00182-009-0169-2.

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9

McKelvey, Richard D., and Thomas R. Palfrey. "Erratum to: Quantal response equilibria for extensive form games." Experimental Economics 18, no. 4 (October 23, 2015): 762–63. http://dx.doi.org/10.1007/s10683-015-9471-y.

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10

Tumennasan, Norovsambuu. "To err is human: Implementation in quantal response equilibria." Games and Economic Behavior 77, no. 1 (January 2013): 138–52. http://dx.doi.org/10.1016/j.geb.2012.10.004.

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11

Farina, Gabriele, Christian Kroer, and Tuomas Sandholm. "Online Convex Optimization for Sequential Decision Processes and Extensive-Form Games." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 1917–25. http://dx.doi.org/10.1609/aaai.v33i01.33011917.

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Regret minimization is a powerful tool for solving large-scale extensive-form games. State-of-the-art methods rely on minimizing regret locally at each decision point. In this work we derive a new framework for regret minimization on sequential decision problems and extensive-form games with general compact convex sets at each decision point and general convex losses, as opposed to prior work which has been for simplex decision points and linear losses. We call our framework laminar regret decomposition. It generalizes the CFR algorithm to this more general setting. Furthermore, our framework enables a new proof of CFR even in the known setting, which is derived from a perspective of decomposing polytope regret, thereby leading to an arguably simpler interpretation of the algorithm. Our generalization to convex compact sets and convex losses allows us to develop new algorithms for several problems: regularized sequential decision making, regularized Nash equilibria in zero-sum extensive-form games, and computing approximate extensive-form perfect equilibria. Our generalization also leads to the first regret-minimization algorithm for computing reduced-normal-form quantal response equilibria based on minimizing local regrets. Experiments show that our framework leads to algorithms that scale at a rate comparable to the fastest variants of counterfactual regret minimization for computing Nash equilibrium, and therefore our approach leads to the first algorithm for computing quantal response equilibria in extremely large games. Our algorithms for (quadratically) regularized equilibrium finding are orders of magnitude faster than the fastest algorithms for Nash equilibrium finding; this suggests regret-minimization algorithms based on decreasing regularization for Nash equilibrium finding as future work. Finally we show that our framework enables a new kind of scalable opponent exploitation approach.

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12

GOEREE, JACOB K., and CHARLES A. HOLT. "An Explanation of Anomalous Behavior in Models of Political Participation." American Political Science Review 99, no. 2 (May 2005): 201–13. http://dx.doi.org/10.1017/s0003055405051609.

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This paper characterizes behavior with “noisy” decision making for models of political interaction characterized by simultaneous binary decisions. Applications include: voting participation games, candidate entry, the volunteer's dilemma, and collective action problems with a contribution threshold. A simple graphical device is used to derive comparative statics and other theoretical properties of a “quantal response” equilibrium, and the resulting predictions are compared with Nash equilibria that arise in the limiting case of no noise. Many anomalous data patterns in laboratory experiments based on these games can be explained in this manner.

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13

Perera, Ryle S. "An Evolutionary Game Theory Strategy for Carbon Emission Reduction in the Electricity Market." International Game Theory Review 20, no. 04 (November 18, 2018): 1850008. http://dx.doi.org/10.1142/s0219198918500081.

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We study how a government can manage a policy of environmental sustainability in a competitive electricity market. We assume that the government plays a Stackelberg game as leader, to study the evolutionary stable equilibria of the problem under this game theory paradigm. We then analyze a bimatrix coordination game to have many equilibria when no single power plant has incentives to deviate when the others reduce carbon emissions. In fact for power plants the adapted behavior is to avoid heavy tariffs, preserve the market share and minimize the environmental impact. We use the notion of quantal response equilibrium (QRE) in the case of bounded rationality to obtain a unique Nash equilibrium known as the centroid-dominant equilibrium of the game. This proposed quantitative framework can be applied by policy makers to determine incentives and tariffs to meet the environmental obligations in the electricity market.

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14

Zhao, Wang, Zhang, Huang, and Gong. "The Game Simulation of “The Belt and Road” Economic and Trade Network Based on the Asymmetric QRE Model." Sustainability 11, no. 12 (June 18, 2019): 3377. http://dx.doi.org/10.3390/su11123377.

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This paper introduces the asymmetric Quantal Response Equilibria (QRE) network game model to explain the influencing factors on the cooperative behavior of "The Belt and Road" countries. The findings suggest that the belief in the sensitivity to own payoff and counterparts, the reward for cooperation by neighbor nodes, the trade facilitation index, and the reduction rate of tariffs were incorporated to have a significant impact on the Belt and Road cooperation. Our findings provide important policy references to the belt and road countries.

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15

Kawagoe, Toshiji, Taisuke Matsubae, and Hirokazu Takizawa. "Quantal response equilibria in a generalized Volunteer’s Dilemma and step-level public goods games with binary decision." Evolutionary and Institutional Economics Review 15, no. 1 (August 22, 2017): 11–23. http://dx.doi.org/10.1007/s40844-017-0081-6.

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16

Leonardos, Stefanos, and Georgios Piliouras. "Exploration-Exploitation in Multi-Agent Learning: Catastrophe Theory Meets Game Theory." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 13 (May 18, 2021): 11263–71. http://dx.doi.org/10.1609/aaai.v35i13.17343.

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Exploration-exploitation is a powerful and practical tool in multi-agent learning (MAL), however, its effects are far from understood. To make progress in this direction, we study a smooth analogue of Q-learning. We start by showing that our learning model has strong theoretical justification as an optimal model for studying exploration-exploitation. Specifically, we prove that smooth Q-learning has bounded regret in arbitrary games for a cost model that explicitly captures the balance between game and exploration costs and that it always converges to the set of quantal-response equilibria (QRE), the standard solution concept for games under bounded rationality, in weighted potential games with heterogeneous learning agents. In our main task, we then turn to measure the effect of exploration in collective system performance. We characterize the geometry of the QRE surface in low-dimensional MAL systems and link our findings with catastrophe (bifurcation) theory. In particular, as the exploration hyperparameter evolves over-time, the system undergoes phase transitions where the number and stability of equilibria can change radically given an infinitesimal change to the exploration parameter. Based on this, we provide a formal theoretical treatment of how tuning the exploration parameter can provably lead to equilibrium selection with both positive as well as negative (and potentially unbounded) effects to system performance.

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17

Friston, Karl, Philipp Schwartenbeck, Thomas FitzGerald, Michael Moutoussis, Timothy Behrens, and Raymond J. Dolan. "The anatomy of choice: dopamine and decision-making." Philosophical Transactions of the Royal Society B: Biological Sciences 369, no. 1655 (November 5, 2014): 20130481. http://dx.doi.org/10.1098/rstb.2013.0481.

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This paper considers goal-directed decision-making in terms of embodied or active inference. We associate bounded rationality with approximate Bayesian inference that optimizes a free energy bound on model evidence. Several constructs such as expected utility, exploration or novelty bonuses, softmax choice rules and optimism bias emerge as natural consequences of free energy minimization. Previous accounts of active inference have focused on predictive coding . In this paper, we consider variational Bayes as a scheme that the brain might use for approximate Bayesian inference. This scheme provides formal constraints on the computational anatomy of inference and action, which appear to be remarkably consistent with neuroanatomy. Active inference contextualizes optimal decision theory within embodied inference, where goals become prior beliefs. For example, expected utility theory emerges as a special case of free energy minimization, where the sensitivity or inverse temperature (associated with softmax functions and quantal response equilibria) has a unique and Bayes-optimal solution. Crucially, this sensitivity corresponds to the precision of beliefs about behaviour. The changes in precision during variational updates are remarkably reminiscent of empirical dopaminergic responses—and they may provide a new perspective on the role of dopamine in assimilating reward prediction errors to optimize decision-making.

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18

Goeree, Jacob K., Charles A. Holt, and Thomas R. Palfrey. "Regular Quantal Response Equilibrium." Experimental Economics 8, no. 4 (December 2005): 347–67. http://dx.doi.org/10.1007/s10683-005-5374-7.

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19

Friedman, Evan. "Endogenous quantal response equilibrium." Games and Economic Behavior 124 (November 2020): 620–43. http://dx.doi.org/10.1016/j.geb.2020.10.003.

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20

He, Qingren, Taiwei Shi, Botao Liu, and Wanhua Qiu. "The Ordering Optimization Model for Bounded Rational Retailer with Inventory Transshipment." Mathematics 10, no. 7 (March 28, 2022): 1079. http://dx.doi.org/10.3390/math10071079.

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In order to study retailers’ ordering behavior deviating from the standard theoretical optimal decision, which is caused by retailers’ information asymmetry, cognitive ability, insufficient computing ability, and other factors, we construct a bounded-rationality choice model with quantal response equilibrium. First, the existence and uniqueness of quantal response equilibrium of transshipment game have been proved with the transshipment price satisfying certain conditions. Then, the numerical example demonstrates that with the increase of bounded-rationality parameters, retailers’ quantal response equilibrium will converge to Nash equilibrium due to the learning effect, and their profits will converge to the profits predicted by standard theory. Finally, the results show that retailers are more averse to the explicit loss of shortage than to the implicit loss of inventory surplus caused by the increase of order quantity. Hence, retailers tend to overorder to avoid loss of shortage.

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21

Scharfenaker, Ellis. "Implications of quantal response statistical equilibrium." Journal of Economic Dynamics and Control 119 (October 2020): 103990. http://dx.doi.org/10.1016/j.jedc.2020.103990.

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22

Selten, Reinhard, Thorsten Chmura, and Sebastian J. Goerg. "Stationary Concepts for Experimental 2 × 2 Games: Reply." American Economic Review 101, no. 2 (April 1, 2011): 1041–44. http://dx.doi.org/10.1257/aer.101.2.1041.

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This is a reply to “Stationary Concepts for Experimental 2 X 2 Games: Comment” by Brunner, Camerer, and Goeree which corrects some computational errors in Selten and Chmura (2008) and extends the comparison of five stationary concepts to data from previous experimental studies. We critically discuss their new findings and relate them to the data of Selten and Chmura (2008). We conclude that the parametric concepts of action-sampling equilibrium and payoff-sampling equilibrium perform better than quantal response equilibrium, and that the non-parametric concept of impulse-balance equilibrium performs at least as well as quantal response equilibrium. (JEL C70)

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23

Allen, Roy, and John Rehbeck. "A Generalization of Quantal Response Equilibrium via Perturbed Utility." Games 12, no. 1 (March 1, 2021): 20. http://dx.doi.org/10.3390/g12010020.

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We present a tractable generalization of quantal response equilibrium via non-expected utility preferences. In particular, we introduce concave perturbed utility games in which an individual has strategy-specific utility indices that depend on the outcome of the game and an additively separable preference to randomize. The preference to randomize can be viewed as a reduced form of limited attention. Using concave perturbed utility games, we show how to enrich models based on logit best response that are common from quantal response equilibrium. First, the desire to randomize can depend on opponents’ strategies. Second, we show how to derive a nested logit best response function. Lastly, we present tractable quadratic perturbed utility games that allow complementarity.

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24

Selten, Reinhard, and Thorsten Chmura. "Stationary Concepts for Experimental 2x2-Games." American Economic Review 98, no. 3 (May 1, 2008): 938–66. http://dx.doi.org/10.1257/aer.98.3.938.

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Five stationary concepts for completely mixed 2x2-games are experimentally compared: Nash equilibrium, quantal response equilibrium, action-sampling equilibrium, payoff-sampling equilibrium (Martin J. Osborne and Ariel Rubinstein 1998), and impulse balance equilibrium. Experiments on 12 games, 6 constant sum games, and 6 nonconstant sum games were run with 12 independent subject groups for each constant sum game and 6 independent subject groups for each nonconstant sum game. Each independent subject group consisted of four players 1 and four players 2, interacting anonymously over 200 periods with random matching. The comparison of the five theories shows that the order of performance from best to worst is as follows: impulse balance equilibrium, payoff-sampling equilibrium, action-sampling equilibrium, quantal response equilibrium, Nash equilibrium. (JEL C70, C91)

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25

Ui, Takashi. "Correlated quantal responses and equilibrium selection." Games and Economic Behavior 57, no. 2 (November 2006): 361–69. http://dx.doi.org/10.1016/j.geb.2005.08.018.

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26

Noti, Gali. "From Behavioral Theories to Econometrics: Inferring Preferences of Human Agents from Data on Repeated Interactions." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 6 (May 18, 2021): 5637–46. http://dx.doi.org/10.1609/aaai.v35i6.16708.

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We consider the problem of estimating preferences of human agents from data of strategic systems where the agents repeatedly interact. Recently, it was demonstrated that a new estimation method called "quantal regret" produces more accurate estimates for human agents than the classic approach that assumes that agents are rational and reach a Nash equilibrium; however, this method has not been compared to methods that take into account behavioral aspects of human play. In this paper we leverage equilibrium concepts from behavioral economics for this purpose and ask how well they perform compared to the quantal regret and Nash equilibrium methods. We develop four estimation methods based on established behavioral equilibrium models to infer the utilities of human agents from observed data of normal-form games. The equilibrium models we study are quantal-response equilibrium, action-sampling equilibrium, payoff-sampling equilibrium, and impulse-balance equilibrium. We show that in some of these concepts the inference is achieved analytically via closed formulas, while in the others the inference is achieved only algorithmically. We use experimental data of 2x2 games to evaluate the estimation success of these behavioral equilibrium methods. The results show that the estimates they produce are more accurate than the estimates of the Nash equilibrium. The comparison with the quantal-regret method shows that the behavioral methods have better hit rates, but the quantal-regret method performs better in terms of the overall mean squared error, and we discuss the differences between the methods.

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27

Rogers, Brian W., Thomas R. Palfrey, and Colin F. Camerer. "Heterogeneous quantal response equilibrium and cognitive hierarchies." Journal of Economic Theory 144, no. 4 (July 2009): 1440–67. http://dx.doi.org/10.1016/j.jet.2008.11.010.

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28

Neri, Claudia. "Quantal response equilibrium in a double auction." Economic Theory Bulletin 3, no. 1 (April 23, 2014): 79–90. http://dx.doi.org/10.1007/s40505-014-0038-4.

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29

Haile, Philip A., Ali Hortaçsu, and Grigory Kosenok. "On the Empirical Content of Quantal Response Equilibrium." American Economic Review 98, no. 1 (February 1, 2008): 180–200. http://dx.doi.org/10.1257/aer.98.1.180.

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The quantal response equilibrium (QRE) notion of Richard D. McKelvey and Thomas R. Palfrey (1995) has recently attracted considerable attention, due in part to its widely documented ability to rationalize observed behavior in games played by experimental subjects. However, even with strong a priori restrictions on unobservables, QRE imposes no falsifiable restrictions: it can rationalize any distribution of behavior in any normal form game. After demonstrating this, we discuss several approaches to testing QRE under additional maintained assumptions. (JEL C72, D84)

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30

Yu, Yue, Jonathan Salfity, David Fridovich-Keil, and Ufuk Topcu. "Inverse Matrix Games With Unique Quantal Response Equilibrium." IEEE Control Systems Letters 7 (2023): 643–48. http://dx.doi.org/10.1109/lcsys.2022.3214857.

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31

Chen, Yin, and Chuangyin Dang. "An extension of quantal response equilibrium and determination of perfect equilibrium." Games and Economic Behavior 124 (November 2020): 659–70. http://dx.doi.org/10.1016/j.geb.2017.12.023.

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32

Ömer, Özlem. "Dynamics of the US Housing Market: A Quantal Response Statistical Equilibrium Approach." Entropy 20, no. 11 (October 30, 2018): 831. http://dx.doi.org/10.3390/e20110831.

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In this article, we demonstrate that a quantal response statistical equilibrium approach to the US housing market with the help of the maximum entropy method of modeling is a powerful way of revealing different characteristics of the housing market behavior before, during and after the recent housing market crash in the US. In this line, a maximum entropy approach to quantal response statistical equilibrium model (QRSE) is employed in order to model housing market dynamics in different phases of the most recent housing market cycle using the S&P Case Shiller housing price index for 20 largest- Metropolitan Regions, and Freddie Mac housing price index (FMHPI) for 367 Metropolitan Cities for the US between 2000 and 2015. Estimated model parameters provide an alternative way to understand and explain the behaviors of economic agents, and market dynamics by questioning the traditional economic theory, which takes assumption for the behavior of rational utility maximizing representative agent with self-fulfilled expectations as given.

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33

Runco, Mariano Gabriel. "What Model Best Describes Initial Choices in a Cournot Duopoly Experiment?" International Journal of Applied Behavioral Economics 5, no. 2 (April 2016): 31–45. http://dx.doi.org/10.4018/ijabe.2016040103.

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This paper tests empirically four models of bounded rationality using data from first responses in a Cournot duopoly experiment. Specifically, the models considered are Level-k, Quantal Response Equilibrium, Noisy Introspection and Logit Cognitive Hierarchy. It is found that the Level-k model (with proportions of Level-0, Level-1 and Level-8 given by 68.5%, 13.2% and 18.3% respectively) provides the best fit in terms of Log-Likelihood and BIC. Moreover, the robustness of our findings is corroborated analyzing subsets of the original data.

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34

Yi, Kang-Oh. "Quantal-response equilibrium models of the ultimatum bargaining game." Games and Economic Behavior 51, no. 2 (May 2005): 324–48. http://dx.doi.org/10.1016/s0899-8256(03)00051-4.

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35

Yi, Kang-Oh. "A quantal response equilibrium model of order-statistic games." Journal of Economic Behavior & Organization 51, no. 3 (July 2003): 413–25. http://dx.doi.org/10.1016/s0167-2681(02)00095-1.

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36

Goeree, Jacob K., Charles A. Holt, and Thomas R. Palfrey. "Quantal Response Equilibrium and Overbidding in Private-Value Auctions." Journal of Economic Theory 104, no. 1 (May 2002): 247–72. http://dx.doi.org/10.1006/jeth.2001.2914.

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37

Shen, Shigen, Keli Hu, Longjun Huang, Hongjie Li, Risheng Han, and Qiying Cao. "Quantal Response Equilibrium-Based Strategies for Intrusion Detection in WSNs." Mobile Information Systems 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/179839.

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This paper is to solve the problem stating that applying Intrusion Detection System (IDS) to guarantee security of Wireless Sensor Networks (WSNs) is computationally costly for sensor nodes due to their limited resources. For this aim, we obtain optimal strategies to save IDS agents’ power, through Quantal Response Equilibrium (QRE) that is more realistic than Nash Equilibrium. A stage Intrusion Detection Game (IDG) is formulated to describe interactions between the Attacker and IDS agents. The preference structures of different strategy profiles are analyzed. Upon these structures, the payoff matrix is obtained. As the Attacker and IDS agents interact continually, the stage IDG is extended to a repeated IDG and its payoffs are correspondingly defined. The optimal strategies based on QRE are then obtained. These optimal strategies considering bounded rationality make IDS agents not always be inDefend. Sensor nodes’ power consumed in performing intrusion analyses can thus be saved. Experiment results show that the probabilities of the actions adopted by the Attacker can be predicted and thus the IDS can respond correspondingly to protect WSNs.

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38

Jessie, Daniel T., and Donald G. Saari. "From the Luce Choice Axiom to the Quantal Response Equilibrium." Journal of Mathematical Psychology 75 (December 2016): 3–9. http://dx.doi.org/10.1016/j.jmp.2015.10.001.

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39

Zhang, Boyu. "Quantal response methods for equilibrium selection in normal form games." Journal of Mathematical Economics 64 (May 2016): 113–23. http://dx.doi.org/10.1016/j.jmateco.2016.04.003.

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40

Scharfenaker, Ellis, and Duncan Foley. "Quantal Response Statistical Equilibrium in Economic Interactions: Theory and Estimation." Entropy 19, no. 9 (August 25, 2017): 444. http://dx.doi.org/10.3390/e19090444.

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41

Brunner, Christoph, Colin F. Camerer, and Jacob K. Goeree. "Stationary Concepts for Experimental 2 × 2 Games: Comment." American Economic Review 101, no. 2 (April 1, 2011): 1029–40. http://dx.doi.org/10.1257/aer.101.2.1029.

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Reinhard Selten and Thorsten Chmura (2008) recently reported laboratory results for completely mixed 2 X 2 games used to compare Nash equilibrium with four other stationary concepts: quantal response equilibrium, action-sampling equilibrium, payoff-sampling equilibrium, and impulse balance equilibrium. We reanalyze their data, correct some errors, and find that Nash clearly fits worst while the four other concepts perform about equally well. We also report new analysis of other previous experiments that illustrate the importance of the loss aversion hardwired into impulse balance equilibrium: when the other non-Nash concepts are augmented with loss aversion, they outperform impulse balance equilibrium.

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42

Hafezalkotob, A., and A. Makui. "Supply Chains Competition under Uncertainty Concerning Player’s Strategies and Customer Choice Behavior: A Generalized Nash Game Approach." Mathematical Problems in Engineering 2012 (2012): 1–29. http://dx.doi.org/10.1155/2012/421265.

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Decision makers in a supply chain confront two main sources of uncertainty in market environment including uncertainty about customers purchasing behaviors and rival chains strategies. Focusing on competition between two supply chains, it is considered that each customer as an independent player selects products of these chains based on random utility model. Similar to quantal response equilibrium approach, we take account of customer rationality as an exogenous parameter. Moreover, it is assumed that decision makers in a supply chain can perceive an estimation of rival strategies about price and service level formulated in the model by fuzzy strategies. In the competition model, chain’s decision makers consider a subjective probability for wining each customer which is formulated by coupled constraints. These constraints connect chains strategies regarding to each customer and yield a generalized Nash equilibrium problem. Since price cutting and increasing service level are main responses to rival supply chain, after calculating optimal strategies, we show that more efficient responses depend on customer preferences.

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43

Zhao, Chuan-Lin, and Hai-Jun Huang. "Modeling Bounded Rationality in Congestion Games with the Quantal Response Equilibrium." Procedia - Social and Behavioral Sciences 138 (July 2014): 641–48. http://dx.doi.org/10.1016/j.sbspro.2014.07.253.

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44

Turocy, Theodore L. "A dynamic homotopy interpretation of the logistic quantal response equilibrium correspondence." Games and Economic Behavior 51, no. 2 (May 2005): 243–63. http://dx.doi.org/10.1016/j.geb.2004.04.003.

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45

Zhang, Boyu, and Josef Hofbauer. "Quantal response methods for equilibrium selection in 2 × 2 coordination games." Games and Economic Behavior 97 (May 2016): 19–31. http://dx.doi.org/10.1016/j.geb.2016.03.002.

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46

Wiener, Noé M. "Labor Market Segmentation and Immigrant Competition: A Quantal Response Statistical Equilibrium Analysis." Entropy 22, no. 7 (July 5, 2020): 742. http://dx.doi.org/10.3390/e22070742.

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Competition between and within groups of workers takes place in labor markets that are segmented along various, often unobservable dimensions. This paper proposes a measure of the intensity of competition in labor markets on the basis of limited data. The maximum entropy principle is used to make inferences about the unobserved mobility decisions of workers in US household data. The quantal response statistical equilibrium class of models can be seen to give robust microfoundations to the persistent patterns of wage inequality. An application to labor market competition between native and foreign-born workers in the United States shows that this class of models captures a substantial proportion of the informational content of observed wage distributions.

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ARAGONES, ENRIQUETA, and THOMAS R. PALFREY. "The Effect of Candidate Quality on Electoral Equilibrium: An Experimental Study." American Political Science Review 98, no. 1 (February 2004): 77–90. http://dx.doi.org/10.1017/s0003055404001017.

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When two candidates of different quality compete in a one-dimensional policy space, the equilibrium outcomes are asymmetric and do not correspond to the median. There are three main effects. First, the better candidate adopts more centrist policies than the worse candidate. Second, the equilibrium is statistical, in the sense that it predicts a probability distribution of outcomes rather than a single degenerate outcome. Third, the equilibrium varies systematically with the level of uncertainty about the location of the median voter. We test these three predictions using laboratory experiments and find strong support for all three. We also observe some biases and show that they can be explained by quantal response equilibrium.

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Wand, Jonathan. "Comparing Models of Strategic Choice: The Role of Uncertainty and Signaling." Political Analysis 14, no. 1 (2006): 101–20. http://dx.doi.org/10.1093/pan/mpi017.

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Testing the fit of competing equilibrium solutions to extensive form games crucially depends on assumptions about the distribution of player types. To illustrate the importance of these assumptions for differentiating standard statistical models of strategic choice, I draw on a game previously analyzed by Lewis and Schultz (2003). The differences that they highlight between a pair of perfect Bayesian equilibrium and quantal response equilibrium models are not produced by signaling and updating dynamics as claimed, but are instead produced by different assumptions about the distribution of player types. The method of analysis developed and the issues raised are applicable to a broad range of structural models of conflict and bargaining.

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Batzilis, Dimitris, Sonia Jaffe, Steven Levitt, John A. List, and Jeffrey Picel. "Behavior in Strategic Settings: Evidence from a Million Rock-Paper-Scissors Games." Games 10, no. 2 (April 10, 2019): 18. http://dx.doi.org/10.3390/g10020018.

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We make use of data from a Facebook application where hundreds of thousands of people played a simultaneous move, zero-sum game—rock-paper-scissors—with varying information to analyze whether play in strategic settings is consistent with extant theories. We report three main insights. First, we observe that most people employ strategies consistent with Nash, at least some of the time. Second, however, players strategically use information on previous play of their opponents, a non-Nash equilibrium behavior; they are more likely to do so when the expected payoffs for such actions increase. Third, experience matters: players with more experience use information on their opponents more effectively than less experienced players, and are more likely to win as a result. We also explore the degree to which the deviations from Nash predictions are consistent with various non-equilibrium models. We analyze both a level-k framework and an adapted quantal response model. The naive version of each these strategies—where players maximize the probability of winning without considering the probability of losing—does better than the standard formulation. While one set of people use strategies that resemble quantal response, there is another group of people who employ strategies that are close to k 1 ; for naive strategies the latter group is much larger.

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Chen, Yefen, Xuanming Su, and Xiaobo Zhao. "Modeling Bounded Rationality in Capacity Allocation Games with the Quantal Response Equilibrium." Management Science 58, no. 10 (October 2012): 1952–62. http://dx.doi.org/10.1287/mnsc.1120.1531.

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