Quantal response equilibria with heterogeneous agents

Abstract

This paper introduces a model of quantal response equilibrium with heterogeneous agents and demonstrates the existence of a representative agent for such populations.Except in rare cases, the representative agent's noise terms cannot be independently and identically distributed across the set of actions, even if that is assumed for the individual agents. This result demonstrates a fundamental difference between a representative agent and truly heterogeneous quantal responders and suggests that when fitting quantal response specifications to aggregate data from a population of subjects, the noise terms should be allowed to be jointly dependent across actions. Even though this introduces additional degrees of freedom, it makes the model well specified. The representative agent inherits a regular quantal response function from the actual agents, so this model does impose falsifiable restrictions.

Uniform Sampling of the Infinite Noncooperative Game on Unit Hypercube and Reshaping Ultimately Multidimensional Matrices of Player’s Payoff Values

“…But with (22), (29), (30) there is the solution (15) distinctive property signifying that both the players' payoffs (21) and the players' NE-strategies supports as hypersurfaces differentiate less as the number S increases. Growing more "stable", the volume and the averaged NEstrategies supports' densities also do not decrease as the number S increases due to (27) and (28). This "nondecreasing" property becomes stronger with (31)- (27) and (32)- (28), strengthening the solution (15) relative independence upon the sampling step within its minimal neighborhood.…”

“…Growing more "stable", the volume and the averaged NEstrategies supports' densities also do not decrease as the number S increases due to (27) and (28). This "nondecreasing" property becomes stronger with (31)- (27) and (32)- (28), strengthening the solution (15) relative independence upon the sampling step within its minimal neighborhood.…”

“…However, NE-solutions render a lot of the refined or modified principles of optimality, allowing to smooth differences in utility and equity [2], [10], [11]. Mainly, they are principles of Pareto equilibrium [2], [6], [8], [10], [13], [14], Mertens-stable equilibrium [15], trembling hand perfect equilibrium [16], proper equilibrium [17], [18], correlated equilibrium [19], sequential equilibrium [20], [21], quasi-perfect equilibrium [18], [22], [23], perfect Bayesian equilibrium [18], [20], [24], [25], quantal response equilibrium [26], [27], self-confirming equilibrium [28], [29], strong Nash equilibrium [30], [31], Markov perfect equilibrium [32], [33]. The question is only to find NEsolutions as fast as possible.…”

“…are true along with (22) and (27). Noting that inequalities (27) and (28) might be stated for the minimally increased sampling step, there is a way to condition the approximate solution harder.…”

“…Noting that inequalities (27) and (28) might be stated for the minimally increased sampling step, there is a way to condition the approximate solution harder. This, nonetheless, will underscore the "monotonicity" of NE-strategies in (15) …”