Game Theory

Game Theory, with core principles, example games, application and discussion.

10 categories of Game Theory with 22 sections in total. The basic idea of Game Theory is explained, with players, strategies, and a payoff matrix. Best responses, dominant and dominated strategies, and a Nash equilibrium are defined and shown. Games with one, multiple, and zero Nash equilibria are presented.

The prisoners’ dilemma is detailed, with its wider implications, and a tit for tat strategy to resolve it in the repeated prisoners’ dilemma form. Backward induction is included, with its potential impact on a tit for tat strategy and its limitations. The results of imperfect information are analysed, as voters in an election don’t know their own expected payoffs, and an employee finds themselves in a different game than they thought with a co-worker.

Asymmetric games are included, where one person has more strategy options than the other, or possesses more power over their own payoffs. First-mover advantage with the Hawk-Dove game, and first-mover disadvantage with the Chicken game, are discussed.

The potential to change your own payoffs or those of others is examined, in the form of dieting and a business attempting to sell its products, as dominant strategies and the outcome of the game are changed. Finally, three alternative ways of playing a game are included. A player acts irrationally and ignores their own payoffs, another bases their strategy on the relative value of their payoffs compared to others, and a third game sees players follow a mixed strategy where probabilities are assigned to their strategies.