Sequential Correlated Equilibria in Stopping Games

Abstract

In many situations, such as trade in stock exchanges, agents have many opportunities to act within a short interval of time. The agents in such situations can often coordinate their actions in advance, but coordination during the game consumes too much time. An equilibrium in such situations has to be sequential in order to handle mistakes made by players. In this paper, we present a new solution concept for infinite-horizon dynamic games, which is appropriate for such situations: a sequential normal-form correlated approximate equilibrium. Under additional assumptions, we show that every such game admits this kind of equilibrium.

Quitting Games and Linear Complementarity Problems

“…This approach can be used together with our result to show that every multiplayer stopping game admits a sunspot ε-equilibrium. The proof is analogous to the proofs in Shmaya and Solan (2004), Heller (2012), and Mashiah-Yaakovi (2014).…”

“…Shmaya and Solan (2004) developed a technique that allows reducing the question of existence of ε-equilibrium in stopping games with integrable payoff processes to the question of existence of ε-equilibrium in quitting games or absorbing games. Heller (2012) and Mashiah-Yaakovi (2014) used the approach of Shmaya and Solan (2004) to prove the existence of normal-form correlated ε-equilibrium in multiplayer stopping games and of subgame-perfect ε-equilibrium in multiplayer stopping games with perfect information, respectively. This approach can be used together with our result to show that every multiplayer stopping game admits a sunspot ε-equilibrium.…”

Construction of Nash equilibrium based on multiple stopping problem in multi-person game

“…The reason for it is diversity of applications of considered models which fit very well the problems present in economic theory and operations research (see, e.g., Heller 2012). This paper has two main contributions with respect to this domain of research.…”

The multi-player nonzero-sum Dynkin game in discrete time

“…Moreover he characterized ε-optimal stopping times. Since this seminal work, the discrete time zeros-sum game has been widely discussed in several settings and works of which one can quote [6,7,11,15,19], etc.…”

“…Nonzero-sum discrete time Dynkin games are also considered in several papers including [4,6,8,9,10,12,13,14,16,17,18] (see also the references therein). However those works, either, they deal only with the case of two players and/or suppose some special structure of the payoffs, or, the strategies of the players are of randomized type.…”