Game Theory

Game theory is a study of analysis of situations in which strategic decisions to be made. The elements of game are: n - player, their strategies and their payoffs.The payoff to each player in general depends on the set of strategies chosen by all the players.

The game can be normal or extensive form. In normal form games, player choose their strategy simulataneoulsy, where as in extensive form, player makes sequential moves.

Prisoner's dilemma game & Criminal's revenge game

In repetitive games, players will cheat if

B > p L T / (1 + r)

B = benefit (short run) from cheating

L = loss each period if cheating is detected

T = number of periods of non-cooperation

P = probability of detection

R = discount factor

In Dominant strategy equilibrium, each player's strategy is optimal regardless of the strategy of the other players.

In Nash equilibrium, strategy of each player is optimal only against each other. Read more detail here.

 

Battle of the sexes

In Game Tree by backward induction method, player can forecast the move of other player. And so knowing about the second player moves, first player can take first-mover advantage.

The solution is that second player become unpredictable by issue a threat. Additionally, threat need to be credible by carrying out the threat. Read more detail here.