scholarly journals A Generalization of Quantal Response Equilibrium via Perturbed Utility

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 20
Author(s):  
Roy Allen ◽  
John Rehbeck
Keyword(s):  
Response Function ◽  
Expected Utility ◽  
Reduced Form ◽  
Limited Attention ◽  
Nested Logit ◽  
Quantal Response ◽  
Quantal Response Equilibrium ◽  
Best Response ◽  
Utility Preferences

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.

Quantal Response Equilibrium in Normal-Form Games

2016 ◽  
Author(s):  
Jacob K. Goeree ◽  
Charles A. Holt ◽  
Thomas R. Palfrey
Keyword(s):  
Normal Form ◽  
Cost Model ◽  
Reduced Form ◽  
Individual Choice ◽  
Response Functions ◽  
Quantal Response ◽  
Quantal Response Equilibrium ◽  
Control Cost ◽  
Normal Form Games ◽  
Best Response

This chapter lays out the general theory of quantal response equilibrium (QRE) for normal-form games. It starts with the reduced-form approach to QR, based on the direct specification of “regular” quantal or smoothed best-response functions required to satisfy four intuitive axioms of stochastic choice. A simple asymmetric matching pennies game is used to illustrate these ideas and show that QRE imposes strong restrictions on the data, even without parametric assumptions on the quantal response functions. Particular attention is given to the logit QRE, since it is the most commonly used approach taken when QRE is applied to experimental or other data. The discussion includes the topological and limiting properties of logit QRE and connections with refinement concepts. QRE is also related to several other equilibrium models of imperfectly rational behavior in games, including a game-theoretic equilibrium version of Luce's (1959) model of individual choice, Rosenthal's (1989) linear response model, and Van Damme's (1987) control cost model; these connections are explained in the chapter.

If It Is Surely Better, Do It More? Implications for Preferences Under Ambiguity

2021 ◽  
Author(s):  
Soheil Ghili ◽  
Peter Klibanoff
Keyword(s):  
Expected Utility ◽  
Ambiguity Aversion ◽  
Upper Bounds ◽  
Maxmin Expected Utility ◽  
Weak Dominance ◽  
Choice Under Uncertainty ◽  
Tight Connection ◽  
Sales Agent ◽  
Utility Preferences ◽  
Sensitive Behavior

Consider a canonical problem in choice under uncertainty: choosing from a convex feasible set consisting of all (Anscombe–Aumann) mixtures of two acts f and g, [Formula: see text]. We propose a preference condition, monotonicity in optimal mixtures, which says that surely improving the act f (in the sense of weak dominance) makes the optimal weight(s) on f weakly higher. We use a stylized model of a sales agent reacting to incentives to illustrate the tight connection between monotonicity in optimal mixtures and a monotone comparative static of interest in applications. We then explore more generally the relation between this condition and preferences exhibiting ambiguity-sensitive behavior as in the classic Ellsberg paradoxes. We find that monotonicity in optimal mixtures and ambiguity aversion (even only local to an event) are incompatible for a large and popular class of ambiguity-sensitive preferences (the c-linearly biseparable class. This implies, for example, that maxmin expected utility preferences are consistent with monotonicity in optimal mixtures if and only if they are subjective expected utility preferences. This incompatibility is not between monotonicity in optimal mixtures and ambiguity aversion per se. For example, we show that smooth ambiguity preferences can satisfy both properties as long as they are not too ambiguity averse. Our most general result, applying to an extremely broad universe of preferences, shows a sense in which monotonicity in optimal mixtures places upper bounds on the intensity of ambiguity-averse behavior. This paper was accepted by Manel Baucells, decision analysis.

Heterogeneity

2016 ◽  
Author(s):  
Jacob K. Goeree ◽  
Charles A. Holt ◽  
Thomas R. Palfrey
Keyword(s):  
Choice Behavior ◽  
Error Rates ◽  
The Other ◽  
Individual Heterogeneity ◽  
Response Functions ◽  
Quantal Response ◽  
Quantal Response Equilibrium ◽  
Skill Levels ◽  
Apparent Reason ◽  
Chess Players

Players have different skills, which has implications for the degree to which they make errors. Low-skill hitters in baseball often swing at bad pitches, beginning skiers frequently fall for no apparent reason, and children often lose at tic-tac-toe. At the other extreme, there are brilliant chess players, bargainers, and litigators who seem to know exactly what move to make or offer to decline. From a quantal response equilibrium (QRE) perspective, these skill levels can be modeled in terms of variation in error rates or in responsiveness of quantal response functions. This chapter explores issues related to individual heterogeneity with respect to player error rates. It also describes some extensions of QRE that relax the assumption that player expectations about the choice behavior of other players are correct. For example, in games that are played only once, players are not able to learn from others' prior decisions, and expectations must be based on introspection. The chapter develops the implications of noisy introspection embedded in a model of iterated thinking.

scholarly journals Measuring Ex Ante Welfare in Insurance Markets

2020 ◽  
Author(s):  
Nathaniel Hendren
Keyword(s):  
Willingness To Pay ◽  
Expected Utility ◽  
Low Income ◽  
Reduced Form ◽  
Cost Curve ◽  
Optimal Insurance ◽  
Percentage Difference ◽  
Ex Ante ◽  
Information Sets ◽  
Market Surplus

Abstract The willingness to pay for insurance captures the value of insurance against only the risk that remains when choices are observed. This article develops tools to measure the ex ante expected utility impact of insurance subsidies and mandates when choices are observed after some insurable information is revealed. The approach retains the transparency of using reduced-form willingness to pay and cost curves, but it adds one additional sufficient statistic: the percentage difference in marginal utilities between insured and uninsured. I provide an approach to estimate this additional statistic that uses only the reduced-form willingness to pay curve, combined with a measure of risk aversion. I compare the approach to structural approaches that require fully specifying the choice environment and information sets of individuals. I apply the approach using existing willingness to pay and cost curve estimates from the low-income health insurance exchange in Massachusetts. Ex ante optimal insurance prices are roughly 30% lower than prices that maximize observed market surplus. While mandates reduce market surplus, the results suggest they would actually increase ex ante expected utility.

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