We show how game-theoretic solution concepts such as Nash equilibrium, correlated equilibrium, rationalizability, and sequential equilibrium can be given a uniform definition in terms of a knowledge-based program with counterfactual semantics. In a precise sense, this program can be viewed as providing a procedural characterization of rationality.
We introduce a natural extension of the notion of swap regret, conditional swap regret, that allows for action modifications conditioned on the player's action history. We prove a series of new results for conditional swap regret minimization. We further extend these results to the case where conditional swaps are considered only for a subset of actions. We also define a new notion of equilibrium, conditional correlated equilibrium, that is tightly connected to the notion of conditional swap regret: when all players follow conditional swap regret minimization strategies, then the empirical distribution approaches this equilibrium. Finally, we extend our results to the multi-armed bandit scenario.
Department of Economics University of Bristol 8 Woodland Road Bristol BS8 1TNFEngland Abstract This paper analyzes automated distributive negotiation where agents have firm deadlines that are private information. The agents are allowed to make and accept offers in any order in continuous time. We show that the only sequential equilibrium outcome is one where the agents walt until the first deadline, at which point that agent concedes everything to the other. This holds for pure and mixed strategies. So, interestingly, rational agents can never agree to a nontrivial split because offers signal enough weakness of bargaining power (early deadline) so that the recipient should never accept. Similarly, the offerer knows that it offered too much if the offer gets accepted: the offerer could have done better by out-waiting the opponent. In most cases, the deadline effect completely overrides time discounting and risk aversion: an agent's payoff does not change with its discount factor or risk attitude. Several implications for the design of negotiating agents are discussed. We also present an effective protocol that implements the equilibrium outcome in dominant strategies. 1 Introduction Multiagent systems for automated negotiation between self-interested agents are becoming increasingly important due to both technology push and application pull. The competitive pressure on the side with many agents often reduces undesirable strategic effects. On the other handFmarket mechanisms often have difficulty in "scaling down" to small numbers of agents (Osborne & Rubinstein 1990). In the limit of one-to-one negotiationFstrategic considerations become prevalent.
We study nonzero-sum hypothesis testing games that arise in the context of adversarial classification, in both the Bayesian as well as the Neyman-Pearson frameworks. We first show that these games admit mixed strategy Nash equilibria, and then we examine some interesting concentration phenomena of these equilibria. Our main results are on the exponential rates of convergence of classification errors at equilibrium, which are analogous to the well-known Chernoff-Stein lemma and Chernoff information that describe the error exponents in the classical binary hypothesis testing problem, but with parameters derived from the adversarial model. The results are validated through numerical experiments.