Hard and soft equilibria in boolean games

A fundamental problem in game theory is the possibility of reaching equilibrium outcomes with undesirable properties, e.g., inefficiency. The economics literature abounds with models that attempt to modify games in order to eliminate such undesirable equilibria, for example through the use of subsidies and taxation, or by allowing players to undergo a preplay negotiation phase. In this paper, we consider the effect of such transformations in Boolean games with costs, where players are primarily motivated to seek the satisfaction of some goal, and are secondarily motivated to minimise the costs of their actions. The preference structure of these games allows us to distinguish between hard and soft equilibria, where hard equilibria arise from goal-seeking behaviour, and cannot be eliminated from games by, e.g., taxes or subsidies, while soft equilibria are those that arise from the desire of agents to minimise costs. We investigate several mechanisms which allow groups of players to form coalitions and eliminate undesirable equilibria from the game, even when taxes or subsidies are not a possibility.