Random Extensive Form Games and its Application to Bargaining

TL;DR

This paper analyzes the asymptotic behavior of outcomes in two-player random extensive form games with uniformly random payoffs, proposing a new solution concept for bargaining based on these results.

Contribution

It introduces a novel approach to bargaining solutions by studying the asymptotic distribution of subgame perfect equilibria in random extensive form games.

Findings

Asymptotic distribution concentrates around a point for certain assignments

Characterization of player assignments affecting outcome concentration

Derivation of a new bargaining solution concept from asymptotic analysis

Abstract

We consider two-player random extensive form games where the payoffs at the leaves are independently drawn uniformly at random from a given feasible set C. We study the asymptotic distribution of the subgame perfect equilibrium outcome for binary-trees with increasing depth in various random (or deterministic) assignments of players to nodes. We characterize the assignments under which the asymptotic distribution concentrates around a point. Our analysis provides a natural way to derive from the asymptotic distribution a novel solution concept for two-player bargaining problems with a solid strategic justification.