Game Manipulators -- the Strategic Implications of Binding Contracts

Commitment devices are powerful tools that can influence and incentivise certain behaviours by linking them to rewards or punishments. These devices are particularly useful in decision-making, as they can steer individuals towards specific choices. In the field of game theory, commitment devices can alter a player's payoff matrix, ultimately changing the game's Nash equilibria. Interestingly, agents, whom we term game manipulators and who can be external to the original game, can leverage such devices to extract fees from players by making them contingent offers that modify the payoffs of their actions. This can result in a different Nash equilibrium with potentially lower payoffs for the players compared to the original game. For this scheme to work, it is required that all commitments be binding, meaning that once an offer is made, it cannot be revoked. Consequently, we analyse binding contracts as the commitment mechanism that enables game manipulation scenarios. The main focus of this study is to formulate the logic of this setting, expand its scope to encompass more intricate schemes, and analyse the behaviour of regret-minimizing agents in scenarios involving game manipulation.