Andriy Zapechelnyuk

Strategic complements and substitutes, and potential games

Abstract We show that games of strategic complements, or substitutes, with aggregation are “pseudo-potential” games. The upshot is that they possess Nash equilibria in pure strategies (NE), even if the strategy sets are not convex; and that various dynamic processes converge to NE. In particular, NE exist in Cournot oligopoly with indivisibilities in production. Our notion of aggregation is quite general and enables us to take a unified view of several disparate models.

PERSUASION OF A PRIVATELY INFORMED RECEIVER

We study persuasion mechanisms in linear environments. A privately informed receiver chooses between two actions. A sender designs a persuasion mechanism that can condition the information disclosed to the receiver on the receiver’s report about his type. We establish the equivalence of implementation by persuasion mechanisms and by experiments. We also characterize the optimal persuasion mechanisms. In particular, if the density of the receiver’s type is log-concave, then the optimal persuasion mechanism reveals the state if and only if the state is below a threshold. We apply our results to the design of media censorship policies.

No-regret Dynamics and Fictitious Play

Potential based no-regret dynamics are shown to be related to fictitious play. Roughly, these are e-best reply dynamics where e is the maximal regret, which vanishes with time. This allows for alternative and sometimes much shorter proofs of known results on convergence of no-regret dynamics to the set of Nash equilibria.

Eliciting information from a committee

The paper addresses the mechanism design problem of eliciting truthful information from a committee of informed experts who collude in their information disclosure strategies. It is shown that under fairly general conditions full information disclosure is possible if and only if the induced outcome is Pareto undominated for the committee members.

OPTIMAL ARBITRATION: OPTIMAL ARBITRATION

We study common arbitration rules for disputes of two privately informed parties, final offer and conventional arbitration. Conventional arbitration is shown to be an optimal arbitration rule in environments with transferable utility, while final offer arbitration is optimal if utility is nontransferable and the parties’ interests are not too aligned. These results explain the prevalence of both arbitration rules in practice.

Decision Making in Uncertain and Changing Environments

We consider an agent who has to repeatedly make choices in an uncertain and changing environment, who has full information of the past, who discounts future payos, but who has no prior. We provide a learning algorithm that

Dynamic benchmark targeting

We study decision making in complex discrete-time dynamic environments where Bayesian optimization is intractable. A decision maker is equipped with a finite set of benchmark strategies. She aims to perform similarly to or better than each of these benchmarks. Furthermore, she cannot commit to any decision rule, hence she must satisfy this goal at all times and after every history. We find such a rule for a sufficiently patient decision maker and show that it necessitates not to rely too much on observations from distant past. In this sense we find that it can be optimal to forget.

Bargaining with a Property Rights Owner

We consider a bargaining problem where one of the players, the intellectual property rights owner (IPRO) can allocate licenses for the use of this property among the interested parties (agents). The agents negotiate with him the allocation of licenses and the payments of the licensees to the IPRO. We state five axioms and characterize the bargaining solutions which satisfy these axioms. In a solution every agent obtains a weighted average of his individually rational level and his marginal contribution to the set of all players, where the weights are the same across all agents and all bargaining problems. The IPRO obtains the remaining surplus. The symmetric solution is the nucleolus of a naturally related coalitional game.