Fictitious Play is a concept from game theory that describes a learning process in strategic situations involving multiple players. In this framework, each player assumes that their opponents’ strategies remain constant and they adjust their own strategies based on the observed actions of these opponents over time. The key idea is that players iteratively play the game, updating their strategies by best responding to the empirical distribution of their opponents’ past actions.
At the start of each round, players choose their actions based on their beliefs about what their opponents will do. After observing the outcomes of these actions, they update their beliefs and strategies accordingly. This process continues until the players converge to a Nash equilibrium, where no player has an incentive to unilaterally change their strategy, as doing so would not yield a better payoff.
Fictitious Play can be particularly useful in environments where players have incomplete information about each other and must learn over time. It has applications in various fields, including economics, artificial intelligence, and auction design. By modeling player behavior and adaptation, fictitious play helps in understanding how strategic interactions evolve and can lead to stable outcomes in competitive scenarios.