Introductory Game Theory: Most Common Types of Games

I recently came across another game theory book, Essentials of Game Theorythat 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.

  1. Normal-form game: The most common game in game theory is the normal-form game where players with different strategies compete with each other for utility maximization. In more mathematical terms, N is a finite set of players where each player is denoted by i. Each player, n_i, has a set of actions available: A_i. For each game, every player may take an action, and the set of all players’ strategies is the vector a where a = A_1 X ... X A_n. The utility obtained is denoted by u = (u_1, ..., u_n) where u_i is the utility received by a player for a particular action A_i -> R for player i.
  2. 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, a \epsilon A_1 X ... X A_n taken by players i and j (where i, j \epsilon N), the utility obtained by both players are the same, u_i(a) = u_j(a).
  3. 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 a \epsilon A_1 X A_2 where A_i is the set of strategies available to player i: the utility for each player obtained from the constant-sum game follows the rule: u_1(a) + u_2(a) = c. In a zero-sum game, c = 0. (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.

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One Response to Introductory Game Theory: Most Common Types of Games

  1. Pingback: Strategies in Normal Games | Sublime Illusions

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