Simultaneous game

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Rock-paper-scissors is an example of a simultaneous game. Roshambo-Laos.jpg
Rock–paper–scissors is an example of a simultaneous game.

In game theory, a simultaneous game or static game [1] is a game where each player chooses their action without knowledge of the actions chosen by other players. [2] Simultaneous games contrast with sequential games, which are played by the players taking turns (moves alternate between players). In other words, both players normally act at the same time in a simultaneous game. Even if the players do not act at the same time, both players are uninformed of each other's move while making their decisions. [ citation needed ] [3] Normal form representations are usually used for simultaneous games.[ citation needed ] Given a continuous game, players will have different information sets if the game is simultaneous than if it is sequential because they have less information to act on at each step in the game. For example, in a two player continuous game that is sequential, the second player can act in response to the action taken by the first player. However, this is not possible in a simultaneous game where both players act at the same time.

Rock-paper-scissors, a widely played hand game, is an example of a simultaneous game. Both players make a decision without knowledge of the opponent's decision, and reveal their hands at the same time. There are two players in this game and each of them has three different strategies to make their decision; the combination of strategy profiles forms a 3×3 table. We will display Player 1's strategies as rows and Player 2's strategies as columns. In the table, the numbers in red represent the payoff to Player 1, the numbers in blue represent the payoff to Player 2. Hence, the pay off for a 2 player game in rock-paper-scissors will look like this:

Player 2

Player 1
RockPaperScissors
Rock
0
0
1
-1
-1
1
Paper
-1
1
0
0
1
-1
Scissors
1
-1
-1
1
0
0

Even though simultaneous games are normally represented in normal form, it can be represented using extensive form too. However, in an extensive form, we must draw one player’s decision before that of the other, but it is important to realize that such representation does not correspond to the actual timing of the players’ decisions. It is important to note that the key to modeling simultaneous game in the extensive form is to get the information sets right. A dashed line between nodes in the extensive form representation of a game represent information asymmetry and specify that, during the game, a party cannot distinguish between the nodes. [4]

Examples of Simultaneous Games Simultaneous game.png
Examples of Simultaneous Games

The prisoner's dilemma is also an example of a simultaneous game. Some variants of chess that belong to this class of games include synchronous chess and parity chess. [5]

See also

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Sequential game class of turn-based game in which one player chooses their action before the others choose theirs

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In game theory, a subgame perfect equilibrium is a refinement of a Nash equilibrium used in dynamic games. A strategy profile is a subgame perfect equilibrium if it represents a Nash equilibrium of every subgame of the original game. Informally, this means that if the players played any smaller game that consisted of only one part of the larger game, their behavior would represent a Nash equilibrium of that smaller game. Every finite extensive game with perfect recall has a subgame perfect equilibrium.

The one-shot deviation principle is the principle of optimality of dynamic programming applied to game theory. It says that a strategy profile of a finite extensive-form game is a subgame perfect equilibrium (SPE) if and only if there exist no profitable one-shot deviations for each subgame and every player. In simpler terms, if no player can increase their payoffs by deviating a single decision, or period, from their original strategy, then the strategy that they have chosen is a SPE. As a result, no player can profit from deviating from the strategy for one period and then reverting to the strategy.

References

  1. Pepall, Lynne, 1952- (2014-01-28). Industrial organization : contemporary theory and empirical applications. Richards, Daniel Jay., Norman, George, 1946- (Fifth ed.). Hoboken, NJ. ISBN   978-1-118-25030-3. OCLC   788246625.CS1 maint: multiple names: authors list (link)
  2. http://www-bcf.usc.edu The Path to Equilibrium in Sequential and Simultaneous Games (Brocas, Carrillo, Sachdeva; 2016).
  3. Managerial Economics: 3 edition. McGraw Hill Education (India) Private Limited. 2018. ISBN   978-93-87067-63-9.
  4. 1 2 Watson, Joel. (2013-05-09). Strategy : an introduction to game theory (Third ed.). New York. ISBN   978-0-393-91838-0. OCLC   842323069.
  5. A V, Murali (2014-10-07). "Parity Chess". Blogger . Retrieved 2017-01-15.

Bibliography