I recently came across another game theory book, Essentials of Game Theory, that introduces the fundamental math concepts behind the discipline. Since I’ve been doing quite a bit of coding over the last few months, I thought it might be a good idea to refresh myself on the math concepts in game theory. Hope this also helps anyone else who wants to learn/relearn the different types of games listed below.
- Normal-form game: The most common game in game theory is the normal-form game where n players with different strategies compete with each other for utility maximization. In more mathematical terms, N is a finite set of n players where each player is denoted by i. Each player, , has a set of actions available: . For each game, every player may take an action, and the set of all players’ strategies is the vector where . The utility obtained is denoted by where is the utility received by a player for a particular action for player .
- Common-payoff game: A game in which players are not competing with each other, but are coordinating on a set of actions that is mutually beneficial for all players. In other words, all the players in a game receive the same utility. Mathematically, given a set of possible actions, taken by players and (where ), the utility obtained by both players are the same, .
- Constant-sum game: This is a subset of the normal-form game in which the utility obtained by all players add to a constant sum. When one player gains in a constant sum game, the other player loses. In other words, in a two-player game, given the set of combinations of possible actions taken by each player where is the set of strategies available to player : the utility for each player obtained from the constant-sum game follows the rule: . In a zero-sum game, . (Note: most constant-sum games you will encounter will be zero-sum games.)
I will be going over definitions for game theory strategies later on this week.