Payoff-relevant State Research Articles

Clock games: Theory and experiments

In many situations, timing is crucial—individuals face a trade-off between gains from waiting versus the risk of being preempted. To examine this, we offer a model of clock games, which we then test experimentally. Each player's clock starts upon receiving a signal about a payoff-relevant state variable. Since the timing of the signals is random, clocks are de-synchronized. A player must decide how long, if at all, to delay his move after receiving the signal. We show that (i) delay decreases as clocks become more synchronized, and (ii) when moves are observable, players “herd” immediately after any player makes a move. Our experimental results are broadly consistent with these two key predictions of the theory.

The Swing Voter's Curse in the Laboratory

This paper reports the first laboratory study of the swing voter's curse and provides insights on the larger theoretical and empirical literature on “pivotal voter” models. Our experiment controls for different information levels of voters, as well as the size of the electorate, the distribution of preferences and other theoretically relevant parameters. The design varies the share of partisan voters and the prior belief about a payoff relevant state of the world. Our results support the equilibrium predictions of the Feddersen-Pesendorfer model. The voters act as if they are aware of the swing voter's curse and adjust their behaviour to compensate. While the compensation is not complete and there is some heterogeneity in individual behaviour, we find that aggregate outcomes, such as efficiency, turnout and margin of victory, closely track the theoretical predictions.

Interactive Epistemology and Solution Concepts for Games with Asymmetric Information

We use an interactive epistemology framework to provide a systematic analysis of some solution concepts for games with asymmetric information. We characterize solution concepts using expressible epistemic assumptions, represented as events in the universal type space generated by primitive uncertainty about the payoff relevant state, payoff irrelevant information, and actions. In most of the paper we adopt an interim perspective, which is appropriate to analyze genuine incomplete information. We relate Delta-rationalizability (Battigalli and Siniscalchi, Advances Theoretical Econ., 2003) to interim correlated rationalizability (Dekel et al., Theoretical Econ., 2007) and to rationalizability in the interim strategic form. We also consider the ex ante perspective, which is appropriate to analyze asymmetric information about an initial chance move. We prove the equivalence between interim correlated rationalizability and an ex ante notion of correlated rationalizability.

Disagreement leads to complete learning: Sequential choice with continuous types

Players with observable, continuous payoff types choose actions sequentially. Players update beliefs about the payoff-relevant state of nature using private signals and information about previous signals in the history of types and actions. Heterogeneity in preferences ensures complete learning.

Uncertainty, co-ordination and path dependence

Our objective is to assess whether dynamics hinder or assist co-ordination in a game with strategic complementarities. We study two dynamic aspects: different agents make decisions at different points in time; and extra information about a payoff-relevant state of nature becomes available over time. We find that the dynamic resolution of information matters most for uniqueness of equilibrium. This is demonstrated by showing that the condition for uniqueness is weaker when learning occurs. We also analyse how successfully agents co-ordinate when there is a unique equilibrium. Finally, we show that path dependence occurs: the order in which signals arrive matters, as well as the total amount of information received.

Goodwill and dynamic advertising strategies

In this paper, we empirically analyze weekly advertising policies of manufacturing firms in consumer goods markets. We assume firms engage in persuasive advertising, thus policies of firms affect the goodwill of a brand. We introduce a demand and a goodwill production function. A simple transformation of the demand function allows us to identify not only the demand parameters but also the parameters of the goodwill production function. We reconstruct the unobserved goodwill levels using these parameters and past advertising levels. We restrict our attention to Markov Perfect Equilibrium (MPE) strategies which are functions of payoff relevant state variables. Without imposing further restrictions on the dynamic competitive environment, we investigate the relationship between observed advertising strategies—which are assumed to be MPE—and payoff relevant state variables by means of several reduced form specifications. The most important determinant of advertising intensity turns out to be goodwill. We demonstrate that controlling for an advertising campaign significantly improves the explanatory power of the model.

Clock Games: Theory and Experiments

Timing is crucial in situations ranging from currency attacks, to product introductions, to starting a revolution. These settings share the feature that payoffs depend critically on the timing of a few other key players - and their moves are uncertain. To capture this, we introduce the notion of clock games and experimentally test them. Each player's clock starts on receiving a signal about a payoff relevant state variable. Since the timing of the signals is random, clocks are de-synchronized. A player must decide how long, if at all, to delay his move after receiving the signal. We show that (i) equilibrium is always characterized by strategic delay - regardless of whether moves are observable or not; (ii) delay decreases as clocks become more synchronized and increases as information becomes more concentrated; (iii) When moves are observable, players herd immediately after any player makes a move. We then show, in a series of experiments, that key predictions of the model are consistent with observed behavior.

Persuasion games with higher-order uncertainty

Shin (J. Econom. Theory 64 (1994) 253–264) showed that a perfectly revealing equilibrium fails to exist in persuasion games when the decision maker is uncertain about the interested party's payoff-relevant information. By explicitly integrating higher-order uncertainty into the information structure, this note shows that a perfectly revealing equilibrium does exist when disclosures are not restrained to intervals of the payoff-relevant state space.

Markov Perfect Equilibria in Repeated Asynchronous Choice Games

This paper examines the issue of multiplicity of equilibria in alternating move repeated games with two players. Such games are canonical models of environments with repeated, asynchronous choices due to inertia or replacement. We focus our attention on Markov Perfect equilibria (MPE). These are Perfect equilibria in which individuals condition their actions on payoff-relevant state variables. Our main result is that the number of Markov Perfect equilibria is generically finite with respect to stage game payoffs. This holds despite the fact that the stochastic game representation of the alternating move repeated game is non-generic in the larger space of state dependent payoffs. We also compare the MPE to non-Markovian equilibria and to the (trivial) MPE of standard repeated games. Unlike the latter, it is often true when moves are asynchronous that Pareto inferior stage game equilibrium payoffs cannot be supported in MPE. Also, MPE can be constructed to support cooperation in a Prisoner's Dilemma despite limited possibilities for constructing punishments.

The rationality and efficacy of decisions under uncertainty and the value of an experiment

A decision maker faces a known prior distribution over payoff relevant states. We compare the expected utility of this individual under two scenarios. In the first, the decision maker makes a choice without further information. In the second, the decision maker has access to an experiment before choosing an action. However, the decision maker does not know the true joint distribution over states and messages. The value of the experiment as measured by the difference in the two utility levels can be negative as well as positive. We give a condition which is necessary and sufficient for the experiment to be valuable in our sense, for any decision problem.

The Burden of Proof in a Game of Persuasion

An arbitrator faces the task of deciding the level of compensation to be received by a plaintiff from a defendant. The arbitrator must rely on the verifiable submissions of the two interested parties. Because the information of the interested parties is not verifiable, the "unravelling argument" has no force. Nevertheless, a class of equilibria of this game gives rise to a particularly simple decision rule for the arbitrator which appeals to a probability distribution over the payoff-relevant state space alone. The uncertainty concerning the precision of the disputants′ information enter as parameters in this distribution. This parametrization yields an answer to how the arbitrator′s decision rule should be modified as the information of the disputants changes. Journal of Economic Literature Classification Numbers: D78, D82, L51.