Yaron Azrieli

Incentives in Experiments: A Theoretical Analysis

Experimental economists currently lack a convention for how to pay subjects in experiments with multiple tasks. We provide a theoretical framework for analyzing this question. Assuming statewise monotonicity and nothing else, we prove that paying for one randomly chosen problem—the random problem selection mechanism—is essentially the only incentive compatible mechanism. Paying for every period is similarly justified when we assume only a “no complementarities at the top” condition. To help experimenters decide which is appropriate for their particular experiment, we discuss empirical tests of these two assumptions.

Lipschitz Games

The Lipschitz constant of a finite normal-form game is the maximal change in some players payoff when a single opponent changes his strategy. We prove that games with small Lipschitz constant admit pure e-equilibria, and pinpoint the maximal Lipschitz constant that is sufficient to imply existence of a pure e-equilibrium as a function of the number of players in the game and the number of strategies of each player. Our proofs use the probabilistic method.

On Pure Conjectural Equilibrium with Non-Manipulable Information

An information structure in a non-cooperative game determines the signal that each player observes as a function of the strategy profile. Such information structure is called non-manipulable if no player can gain new information by changing his strategy. A Conjectural Equilibrium (CE) (Battigalli in Unpublished undergraduate dissertation, 1987; Battigalli and Guaitoli 1988; Decisions, games and markets, 1997) with respect to a given information structure is a strategy profile in which each player plays a best response to his conjecture about his opponents’ play and his conjecture is not contradicted by the signal he observes. We provide a sufficient condition for the existence of pure CE in games with a non-manipulable information structure. We then apply this condition to prove existence of pure CE in two classes of games when the information that players have is the distribution of strategies in the population.

The value of a stochastic information structure

Upon observing a signal, a Bayesian decision maker updates her probability distribution over the state space, chooses an action, and receives a payoff that depends on the state and the action taken. An information structure determines the set of possible signals and the probability of each signal given a state. For a fixed decision problem, the value of an information structure is the maximal expected utility that the decision maker can get when the observed signals are governed by this structure. Thus, every decision problem induces a preference order over information structures according to their value. We characterize preference orders that can be obtained in this way. We also characterize the functions defined over information structures that measure their value.

A bank runs model with a continuum of types

We consider a bank runs model a la Diamond and Dybvig (1983) [3] with a continuum of agent types, indexed by the degree of patience. Much of our understanding based on the two-type model must be modified. The endogenous determination of a cutoff type is central to the analysis. In the case where the bank can credibly commit to a contract, the optimal contract results in socially excessive early withdrawals in every equilibrium of the post-deposit subgame. Thus, even at the best equilibrium the socially efficient outcome is not achieved, and agentsʼ behavior exhibits features of a bank run. In the case where commitment is not possible, there are strictly more early withdrawals and strictly lower welfare than the full-commitment equilibrium.

Dominance-solvable common-value large auctions ✩

We consider second-price common-value auctions with an increasing number of bidders. We define a strategy of bidder i to be (ex-post, weakly) asymptotically dominated if there is another strategy for i that does, in the limit, as well against any sequence of strategies of iʼs opponents, and with positive probability does strictly better against at least one sequence. Our main result provides a sufficient condition on the information structure for the process of iteratively deleting asymptotically dominated strategies to terminate after just two iterations, with only one strategy left for each player. This strategy is fully characterized. We also show that, under standard assumptions, a similar condition to that of Wilson (1977) implies our sufficient condition and therefore implies asymptotic dominance solvability.

On the self-(in)stability of weighted majority rules☆

A voting rule f is self-stable (Barbera and Jackson, 2004) if any alternative rule g does not have sufficient support in the society to replace f, where the decision between f and g is based on the rule f itself. While Barbera and Jackson focused on anonymous rules in which all agents have the same voting power, we consider here the larger class of weighted majority rules. Our main result is a characterization of self-stability in this setup, which shows that only few rules of a very particular form satisfy this criterion. This result provides a possible explanation for the tendency of societies to use more conservative rules when it comes to changing the voting rule. We discuss self-stability in this latter case, where a different rule F may be used to decide between f and g.

Comment on “The Law of Large Demand for Information”

Say that one information structure is eventually Blackwell sufficient for another if, for every large enough n, an n‐sample from the first is Blackwell sufficient (Blackwell (1951, 1954)) for an n‐sample from the second. This note shows that eventual Blackwell sufficiency lies strictly between (one‐shot) Blackwell sufficiency and the ordering of information structures formulated by Moscarini and Smith (2002), and thus offers a new criterion for comparing experiments. A characterization of eventual Blackwell sufficiency in terms of the one‐shot experiments remains an open question.

The price of ‘one person, one vote’

I study the design of binary voting rules in environments where agents are heterogenous either in the stakes that they have in the decision or in the quality of information they possess regarding the correct course of action. The price of ‘one person, one vote’ is defined as the reduction in welfare resulting from constraining the voting rule to treat the agents symmetrically. I analyze how this price depends on the parameters of the environment, particularly on the level of heterogeneity in the society. The results shed light on the tradeoff between equality and efficiency in the context of constitutional design.