Lost in Translation? Basis Utility and Proportionality in Games

Cooperative and noncooperative games have no representation of players's basis utilities. Basis utility is the natural reference point on a player's utility scale that enables the determination the marginal utility of any payoff or allocation. A player's basis utility can be determined by an observer and other players under standard rationality assumptions. Basis utility allows interpersonal comparison of proportional utility gains relative to the disagreement outcome. Proportional bargaining is the unique monotonic, affine transformation invariant, efficient, individually rational and symmetric solution in pure bargaining games with basis utility. The cooperative soft equal split solution results when individual rationality is not required and aspirations are considered part of the bargaining problem. The noncooperative rationality of these results is demonstrated with a proportional bargaining based on Gul (1988). Further noncooperative application is demonstrated by showing that quantal response equilibria with multiplicative error structures (Goeree, Holt and Palfrey (2004)) become translation invariant with specification of basis utility. Recognition of basis utility results in a robust family of monotonic pure bargaining solutions comprising the soft equal split, Kalai-Smorodinsky (1975) and proportional solutions