Players in a game are “in equilibrium ” if they are rational, and accurately predict other players ’ strategies. In many experiments, however, players are not in equilibrium. An alternative is “cognitive hierarchy ” (CH) theory, where each player assumes that his strategy is the most sophisticated. The CH model has inductively defined strategic categories: step 0 players randomize; and step k thinkers best-respond, assuming that other players are distributed over step 0 through step k � 1. This model fits empirical data, and explains why equilibrium theory predicts behavior well in some games and poorly in others. An average of 1.5 steps fits data from many games. I.

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 apriorirestrictions 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, C52, C90) The quantal response equilibrium (QRE) notion of McKelvey and Palfrey (1995) can be viewed as an extension of standard random utility models of discrete (“quantal”) choice to strategic settings, or as a generalization of Nash equilibrium that allows noisy optimizing behavior while maintaining the internal consistency of rational expectations. Formally, QRE is based on the introduction of random perturbations to the payoffs associated with each action a player can take. 1 Realizations of these perturbations affect which action is the best response to the equilibrium distribution of opponents ’ behavior. 1We give a more complete discussion in the following section. The literature has considered generalizations of the QRE to extensive form games (McKelvey and Palfrey (1998)) and games with continuous strategy

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In order to succeed, agents playing games must reason about the mechanics of the game, the strategies of other agents, other agents' reasoning about their strategies, and the rationality of agents. This paper presents a compact, natural and highly expressive language for reasoning about the beliefs and rationality of agents' decision-making processes in games. It extends a previous version of the language in a number of important ways. Agents can reason directly about the rationality of other agents; agents' beliefs are allowed to conflict with one another, including situations in which these beliefs form a cyclic structure; agents' play can deviate from the normative game theoretic solution. The paper formalizes the equilibria that holds with respect to agents' models and behavior, and provides algorithms for computing it. It also shows that the language is strictly more expressive than that of Bayesian games.

www.elsevier.com/locate/geb Self-referential thinking and equilibrium as states of mind in games: fMRI evidence ✩

In some strategic games, thinking ahead about other players’ reasoning can lead to better predictions about what they will do. In other games, infinitely iterated reasoning ultimately prescribes random play. In an online experiment of strategic thinking in groups, we tested participants in a game with the formal structure of a random game, but the superficial structure of a game that rewards iterated reasoning. We found that participants conformed to the superficial structure of the game, and earned more than they would have by playing randomly. We estimated how many steps participants thought ahead in the game and discovered implicit coordination at the group level. Participants unexpectedly “matched ” their degree of iterated thinking to each other.

Self-referential thinking and equilibrium as states of mind in games: fMRI evidence ✩ 8 8

Recent advances in shopper insights reveal that consumers rarely “shop ” the entire store. On average, shoppers ’ paths only cover about one-third of the areas in a grocery store and hence are unexposed to the majority of products in the store. Given that shoppers typically use physical products in the store as an external memory cue, encouraging shoppers to travel more of the store may increase unplanned spending. Estimating the direct effect of in-store travel distance on unplanned spending, however, is complicated due to the difficulty of collecting in-store path data and the endogeneity of in-store travel distance. To address both issues, we collect a novel dataset using in-store RFID tracking that measures in-store travel distance accurately, and develop an instrumental variable approach to account for endogeneity. Our estimates suggest that the elasticity of unplanned spending on travel distance is 1.57, which is 57 % higher than the uncorrected OLS estimate. Further, we apply our estimates to assess the effectiveness of two strategies that encourage longer shopping paths. We find that changing the locations of three destination categories can increase unplanned spending by 7.2%, while strategically promoting