Subgame-perfect equilibria in stochastic timing games

Abstract: We develop a notion of subgames and the related notion of subgame-perfect equilibrium – possibly in mixed strategies – for stochastic timing games. To capture all situations that can arise in continuous-time models, it is necessary to consider stopping times as the starting dates of subgames. We generalize Fudenberg and Tirole’s (1985) mixed-strategy extensions to make them applicable to stochastic timing games and thereby provide a sound basis for subgame-perfect equilibria of preemption games. Sufficient conditions for equilibrium existence are presented, and examples illustrate their application as well as the fact that intuitive arguments can break down in the presence of stochastic processes with jumps

Subgame-Perfect Equilibria in Stochastic Timing Games

We introduce a notion of subgames for stochastic timing games and the related notion of subgame-perfect equilibrium in possibly mixed strategies. While a good notion of subgame-perfect equilibrium for continuous-time games is not available in general, we argue that our model is the appropriate version for timing games. We show that the notion coincides with the usual one for discrete-time games. Many timing games in continuous time have only equilibria in mixed strategies -- in particular preemption games, which often occur in the strategic real option literature. We provide a sound foundation for some workhorse equilibria of that literature, which has been lacking as we show. We obtain a general constructive existence result for subgame-perfect equilibria in preemption games and illustrate our findings by several explicit applications.Comment: 27 pages, 1 figur

Multistage Game Models and Delay Supergames

Prize Lecture to the memory of Alfred Nobel, December 9, 1994.Game Theory;

Deterministic Multi-Player Dynkin Games

A multi-player Dynkin game is a sequential game in which at every stage one of the players is chosen, and that player can decide whether to continue the game or to stop it, in which case all players receive some terminal payoff. We study a variant of this model, where the order by which players are chosen is deterministic, and the probability that the game terminates once the chosen player decides to stop may be strictly less than one. We prove that a subgame-perfect e-equilibrium in Markovian strategies exists. If the game is not degenerate this e-equilibrium is actually in pure strategies.n-player games; stopping games; subgame perfect equilibrium

On the Rationality of Escalation

Escalation is a typical feature of infinite games. Therefore tools conceived for studying infinite mathematical structures, namely those deriving from coinduction are essential. Here we use coinduction, or backward coinduction (to show its connection with the same concept for finite games) to study carefully and formally the infinite games especially those called dollar auctions, which are considered as the paradigm of escalation. Unlike what is commonly admitted, we show that, provided one assumes that the other agent will always stop, bidding is rational, because it results in a subgame perfect equilibrium. We show that this is not the only rational strategy profile (the only subgame perfect equilibrium). Indeed if an agent stops and will stop at every step, we claim that he is rational as well, if one admits that his opponent will never stop, because this corresponds to a subgame perfect equilibrium. Amazingly, in the infinite dollar auction game, the behavior in which both agents stop at each step is not a Nash equilibrium, hence is not a subgame perfect equilibrium, hence is not rational.Comment: 19 p. This paper is a duplicate of arXiv:1004.525

Volunteering a Public Service: An Experimental Investigation

In some public goods environments it may be advantageous for heterogeneous groups to be coordinated by a single individual. This “volunteer” will bear private costs for acting as the leader while enabling each member of the group to achieve maximum potential gains. This environment is modeled as a War of Attrition game in which everyone can wait for someone else to volunteer. Since these games generally have multiple Nash equilibria but a unique subgameperfect equilibrium, we tested experimentally the predictive power of the subgame-perfection criterion. Our data contradict that subjects saw the subgame-perfect strategy combination as the obvious way to play the game. An alternative behavioral hypothesis – that subjects were unable to predict accurately how their opponents would play and tried to maximize their expected payoff – is proposed. This hypothesis fits the observed data generally well.

Single-Agent and Mean-Field Time-Inconsistent Stopping Problems in Discrete Time

In this thesis, we first consider single-agent time-inconsistent stopping problems under non-exponential discounting in discrete time with infinite horizon. We extend the iterative approach introduced by Huang and Zhou (2017) to time-inhomogeneous setting and establish the existence of nonstationary subgame perfect Nash equilibria. Under certain continuity assumptions, we further show the existence of a unique optimal equilibrium which dominates any other equilibria pointwisely. Explicit examples of time-homogeneous model with time-inhomogeneous equilibria are also constructed. We then apply the single-agent results to mean field stopping games where each agent plays against other agents as well as against future selves. We construct a single-agent optimal equilibrium for each fixed mean field interaction represented by the proportion of players that have stopped at each time and use this to show the existence of two-layer equilibria in two examples of mean field time-inconsistent stopping games