Choice-Nash Equilibria

We provide existence results for equilibria of games where players employ abstract (non binary) choice rules. Such results are shown to encompass as a relevant instance that of games where players have (non-transitive) SSB (Skew-Symmetric Bilinear) preferences, as will as other well-known transitive (e. g. Nash´s) and non-transitive (e. g. Shafer and Sonnenschein´s) models in the literature. Further, our general model contains games where players display procedural rationality.

Does Choice Change Preferences? An Incentivized Test of the Mere Choice Effect

Widespread evidence from psychology and neuroscience documents that previous choices unconditionally increase the later desirability of chosen objects, even if those choices were uninformative. This is problematic for economists who use choice data to estimate latent preferences, demand functions, and social welfare. The evidence on this mere choice effect, however, exhibits serious shortcomings which prevent evaluating its possible relevance for economics. In this paper, we present a novel, parsimonious experimental design to test for the economic validity of the mere choice effect addressing these shortcomings. Our design uses well-defined, monetary lotteries, all decisions are incentivized, and we effectively randomize participants’ initial choices without relying on deception. Results from a large, pre-registered online experiment find no support for the mere choice effect. Our results challenge conventional wisdom outside economics. The mere choice effect does not seem to be a concern for economics, at least in the domain of decision making under risk.</p

Characterizations of perfect recall

This paper considers the condition of perfect recall for the class of arbitrarily large discrete extensive form games. The known definitions of perfect recall are shown to be equivalent even beyond finite games. Further, a qualitatively new characterization in terms of choices is obtained. In particular, an extensive form game satisfies perfect recall if and only if the set of choices, viewed as sets of ultimate outcomes, fulfill the Trivial Intersection property, that is, any two choices with nonempty intersection are ordered by set inclusion

Local interactions under switching costs

We study the impact of switching costs on the long-run outcome in 2×2 coordination games played in the circular city model of local interactions. For low levels of switching costs, the predictions are in line with the previous literature and the risk-dominant convention is the unique long-run equilibrium. For intermediate levels of switching costs, the set of long-run equilibria still contain the risk-dominant convention but may also contain conventions that are not risk dominant. The set of long-run equilibria may further be non-monotonic in the level of switching costs, i.e., as switching costs increase the prediction that the risk-dominant convention is the unique long-run equilibrium and the prediction that both conventions are long-run equilibria alternate. Finally, for high levels of switching costs, also non-monomorphic states will be included in the set of long-run equilibria

Unbeatable Imitation

We show that for many classes of symmetric two-player games, the simple decision rule "imitate-the-best" can hardly be beaten by any other decision rule. We provide necessary and sufficient conditions for imitation to be unbeatable and show that it can only be beaten by much in games that are of the rock-scissors-paper variety. Thus, in many interesting examples, like 2x2 games, Cournot duopoly, price competition, rent seeking, public goods games, common pool resource games, minimum effort coordination games, arms race, search, bargaining, etc., imitation cannot be beaten by much even by a very clever opponent

Metastability of Asymptotically Well-Behaved Potential Games

One of the main criticisms to game theory concerns the assumption of full rationality. Logit dynamics is a decentralized algorithm in which a level of irrationality (a.k.a. "noise") is introduced in players' behavior. In this context, the solution concept of interest becomes the logit equilibrium, as opposed to Nash equilibria. Logit equilibria are distributions over strategy profiles that possess several nice properties, including existence and uniqueness. However, there are games in which their computation may take time exponential in the number of players. We therefore look at an approximate version of logit equilibria, called metastable distributions, introduced by Auletta et al. [SODA 2012]. These are distributions that remain stable (i.e., players do not go too far from it) for a super-polynomial number of steps (rather than forever, as for logit equilibria). The hope is that these distributions exist and can be reached quickly by logit dynamics. We identify a class of potential games, called asymptotically well-behaved, for which the behavior of the logit dynamics is not chaotic as the number of players increases so to guarantee meaningful asymptotic results. We prove that any such game admits distributions which are metastable no matter the level of noise present in the system, and the starting profile of the dynamics. These distributions can be quickly reached if the rationality level is not too big when compared to the inverse of the maximum difference in potential. Our proofs build on results which may be of independent interest, including some spectral characterizations of the transition matrix defined by logit dynamics for generic games and the relationship of several convergence measures for Markov chains

Preference reversals: Time and again

This paper sheds new light on the preference reversal phenomenon by analyzing decision times in the choice task. In a first experiment, we replicated the standard reversal pattern and found that choices associated with reversals take significantly longer than non-reversals, and non-reversal choices take longer whenever long-shot lotteries are selected. These results can be explained by a combination of noisy lottery evaluations (imprecise preferences) and an overpricing phenomenon associated with the compatibility hypothesis. The first cause explains the existence of reversals, while the second explains the predominance of a particular type thereof. A second experiment showed that the overpricing phenomenon can be shut down, greatly reducing reversals, by using ranking-based, ordinally-framed evaluation tasks. This experiment also disentangled the two determinants of reversals, because imprecise evaluations still deliver testable predictions on decision times even in the absence of the overpricing phenomenon. Strikingly, when unframed ranking tasks were used, decision times in the choice phase were greatly reduced, even though this phase was identical across treatments. This observation is consistent with psychological insights on conflicting decision processes

The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms

The literature specifies extensive-form games in many styles, and eventually I hope to formally translate games across those styles. Toward that end, this paper defines $\mathbf{NCF}$, the category of node-and-choice forms. The category's objects are extensive forms in essentially any style, and the category's isomorphisms are made to accord with the literature's small handful of ad hoc style equivalences. Further, this paper develops two full subcategories: $\mathbf{CsqF}$ for forms whose nodes are choice-sequences, and $\mathbf{CsetF}$ for forms whose nodes are choice-sets. I show that $\mathbf{NCF}$ is "isomorphically enclosed" in $\mathbf{CsqF}$ in the sense that each $\mathbf{NCF}$ form is isomorphic to a $\mathbf{CsqF}$ form. Similarly, I show that $\mathbf{CsqF_{\tilde a}}$ is isomorphically enclosed in $\mathbf{CsetF}$ in the sense that each $\mathbf{CsqF}$ form with no-absentmindedness is isomorphic to a $\mathbf{CsetF}$ form. The converses are found to be almost immediate, and the resulting equivalences unify and simplify two ad hoc style equivalences in Kline and Luckraz 2016 and Streufert 2019. Aside from the larger agenda, this paper already makes three practical contributions. Style equivalences are made easier to derive by [1] a natural concept of isomorphic invariance and [2] the composability of isomorphic enclosures. In addition, [3] some new consequences of equivalence are systematically deduced.Comment: 43 pages, 9 figure

Independent Lazy Better-Response Dynamics on Network Games

International audienceWe study an independent best-response dynamics on network games in which the nodes (players) decide to revise their strategies independently with some probability. We provide several bounds on the convergence time to an equilibrium as a function of this probability, the degree of the network, and the potential of the underlying games. These dynamics are somewhat more suitable for distributed environments than the classical better- and best-response dynamics where players revise their strategies "sequentially'", i.e., no two players revise their strategies simultaneously