Optimal Auctions with Simultaneous and Costly Participation

We study the optimal auction problem with participation costs in the symmetric independent private values setting, where bidders know their valuations when they make independent participation decisions. After characterizing the optimal auction in terms of participation cutoffs, we provide an example where it is asymmetric. We then investigate when the optimal auction will be symmetric/asymmetric and the nature of possible asymmetries. We also show that, under some conditions, the seller obtains her maximal profit in an (asymmetric) equilibrium of an anonymous second price auction. In general, the seller can also use non-anonymous auctions that resemble the ones that are actually observed in practice.

Ratifiability of Efficient Collusive Mechanisms in Second-Price Auctions with Participation Costs

We investigate whether efficient collusive bidding mechanisms are affected by potential information leakage from bidders' decisions to participate in them within the independent private values setting. We apply the concept of ratifiability introduced by Cramton and Palfrey (1995) and show that when the seller uses a second-price auction with participation costs, the standard efficient cartel mechanisms such as preauction knockouts analyzed in the literature will not be ratified by cartel members. A high-value bidder benefits from vetoing the cartel mechanism since doing so sends a credible signal that she has high value, which in turn discourages other bidders from bidding in the seller's auction.Auctions, collusion, ratifiability

Evolution of Preferences

We model, using evolutionary game theory, the implications of endogenous determination of preferences over the outcomes of any given two-player normal form game, G. We consider a large population randomly and repeatedly matched to play G. Each individual has a preference relation over the outcomes of G which may be different than the "true" payoff function in G, and makes optimal choices given her preferences. The evolution of preferences is driven by the payoffs in G that each player obtains. We define stable outcomes (of G) as arising from the stable points of the evolutionary process described above. In our most general model players know the distribution of preferences in the population and observe their opponents' preferences with probability p. They then play a (Bayesian) Nash equilibrium of the resulting game of incomplete information. In the case in which players can perfectly observe their opponents' preferences, i.e., p=1, (where the game is actually one of complete information) an outcome is stable only if it is efficient. Also, an efficient outcome which arises from a strict Nash equilibrium is stable. We also characterize, for 2×2 games, both the stable outcomes and the stable distributions of preferences in the population. When preferences are unobservable, i.e., p=0, we show that stability in our model of evolution of preferences coincides with the notion of neutrally stable strategy (NSS). Finally, we consider robustness of these results. The necessity and sufficiency results are robust to slight changes in p, except for the sufficiency of NSS when p=0: There are in fact (Pareto-inferior) risk-dominant strict equilibria that are not stable for any p>0.Evolution of preferences, observability

Cooperation, Secret Handshakes, and Imitation in the Prisoners' Dilemma

In the prisoners' dilemma game, the only evolutionary stable strategy is defection, even though nutual cooperation yields a higher payoff. Building on a paper by Robson (1990), we introduce mutants who have the ability to send a (costly) signal, i.e., the "secret handshake," before each round of the game and to condition their actions on whether or not they observe the same signal from their opponent. A population playing the strategy "always defect" is vulnerable to secret handshake mutants who cooperate when they meet other secret handshakers and defect against tother opponents. However, these secret handshakers are in turn vulberable ot a second round of mutants who imitate the secret handshake and then defect against all opponents. But now a new group of secret handshakers with a different secret handshake can arise. Thus, play can cycle between cooperation and defection. We study the dynamics of that cycling. We show that in the limit, as the probability of mutation goes to zero, cooperation occurs on average half the time. Using simulations to study the implications of our model when the mutation probability is larger than zero, we find that it is possible for cooperation to be sustained for long periods. In general, cooperation is favored when mutual cooperation has aj large payoff advantage over mutual defection, and when the payoff advantage of unilateral defection is small. Surprisingly, however, there are cases where an increased payoff to unilateral defection actually raises the level of cooperation.

Nash Equilibrium and the Evolution of Preferences

A population of players of players is randomly matched to play a normal form game G. The payoffs in this game represent the fitness associated with the various outcomes. Each individual has preferences over the outcomes in the game and chooses an optimal action with respect to those preferences. However, these preferences needn't coincide withe the fitness payoffs. When evolution selects individuals on the basis of the fitness of the actions they choose, the distribution of aggregate play must be a Nash equilibrium of G. Weak additional assumptions on the evolutionary process imply perfect equilibrium.

A model of evidence production and optimal standard of proof and penalty in criminal trials

The defendant is either innocent or guilty, which she, not the court or prosecutor, knows. The court convicts the defendant whenever its posterior probability of her guilt - which depends on the evidence presented - is greater than . Evidence production by litigating parties is a costly stochastic process. Subsequently, the optimal choice of standard of proof and penalty is analysed. The optimal standard of proof is increasing in the cost of convicting an innocent defendant and decreasing in the cost of acquitting a guilty defendant. Higher penalties may increase probabilities of false conviction false acquittal.