Mixed Capability Games

TL;DR

This paper introduces mixed capability games, a new class of strategic games modeling how varying player capabilities, such as strategy space size, influence game outcomes, with a focus on a specific variant of the Gold and Mines Game.

Contribution

It defines mixed capability games, models player capabilities as strategy space size, and derives a closed-form capability transfer function for a specific game variant.

Findings

Derived a closed-form capability transfer function for the mixed capability Gold and Mines Game.

Provided a framework to analyze how different player capabilities affect game dynamics.

Established a foundation for future studies on capability impacts in strategic games.

Abstract

We present a new class of strategic games, mixed capability games, as a foundation for studying how different player capabilities impact the dynamics and outcomes of strategic games. We analyze the impact of different player capabilities via a capability transfer function that characterizes the payoff of each player at equilibrium given capabilities for all players in the game. In this paper, we model a player's capability as the size of the strategy space available to that player. We analyze a mixed capability variant of the Gold and Mines Game recently proposed by Yang et al. and derive its capability transfer function in closed form.