Transformations of normal form games by preplay offers for payments among players

TL;DR

This paper analyzes how binding preplay offers for payments among players can transform the payoff matrix of normal form games, providing a complete characterization of such transformations.

Contribution

It offers a comprehensive analysis and characterization of payoff matrix transformations induced by preplay offers in normal form games.

Findings

Complete characterization of payoff transformations

Conditions under which transformations occur

Implications for strategic behavior

Abstract

We consider transformations of normal form games by binding preplay offers of players for payments of utility to other players conditional on them playing designated in the offers strategies. The game-theoretic effect of such preplay offers is transformation of the payoff matrix of the game by transferring payoffs between players. Here we analyze and completely characterize the possible transformations of the payoff matrix of a normal form game by sets of preplay offers.