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- Matching_pennies abstract "Matching pennies is the name for a simple example game used in game theory. It is the two strategy equivalent of Rock, Paper, Scissors. Matching pennies is used primarily to illustrate the concept of mixed strategies and a mixed strategy Nash equilibrium.The game is played between two players, Player A and Player B. Each player has a penny and must secretly turn the penny to heads or tails. The players then reveal their choices simultaneously. If the pennies match (both heads or both tails) Player A keeps both pennies, so wins one from Player B (+1 for A, -1 for B). If the pennies do not match (one heads and one tails) Player B keeps both pennies, so receives one from Player A (-1 for A, +1 for B). This is an example of a zero-sum game, where one player's gain is exactly equal to the other player's loss.The game can be written in a payoff matrix (pictured right). Each cell of the matrix shows the two players' payoffs, with Player A's payoffs listed first.This game has no pure strategy Nash equilibrium since there is no pure strategy (heads or tails) that is a best response to a best response. In other words, there is no pair of pure strategies such that neither player would want to switch if told what the other would do. Instead, the unique Nash equilibrium of this game is in mixed strategies: each player chooses heads or tails with equal probability. In this way, each player makes the other indifferent between choosing heads or tails, so neither player has an incentive to try another strategy. The best response functions for mixed strategies are depicted on the figure 1 below:The matching pennies game is mathematically equivalent to the games "Morra" or "odds and evens", where two players simultaneously display one or two fingers, with the winner determined by whether or not the number of fingers match. Again, the only strategy for these games to avoid being exploited is to play the equilibrium.Of course, human players might not faithfully apply the equilibrium strategy, especially if matching pennies is played repeatedly. In a repeated game, if one is sufficiently adept at psychology, it may be possible to predict the opponent's move and choose accordingly, in the same manner as expert Rock, Paper, Scissors players. In this way, a positive expected payoff might be attainable, whereas when either player plays the equilibrium, everyone's expected payoff is zero.Nonetheless, statistical analysis of penalty kicks in soccer—a high-stakes real-world situation that closely resembles the matching pennies game—has shown that the decisions of kickers and goalies resemble a mixed strategy equilibrium.".
- Matching_pennies thumbnail Reaction-correspondence-matching-pennies.jpg?width=300.
- Matching_pennies wikiPageID "1369392".
- Matching_pennies wikiPageLength "4595".
- Matching_pennies wikiPageOutDegree "19".
- Matching_pennies wikiPageRevisionID "609401147".
- Matching_pennies wikiPageWikiLink Best_response.
- Matching_pennies wikiPageWikiLink Category:Game_theory.
- Matching_pennies wikiPageWikiLink Expected_value.
- Matching_pennies wikiPageWikiLink Game_theory.
- Matching_pennies wikiPageWikiLink Mixed_strategy.
- Matching_pennies wikiPageWikiLink Morra_(game).
- Matching_pennies wikiPageWikiLink Nash_equilibrium.
- Matching_pennies wikiPageWikiLink Normal-form_game.
- Matching_pennies wikiPageWikiLink Odd_or_Even.
- Matching_pennies wikiPageWikiLink Odds_and_evens.
- Matching_pennies wikiPageWikiLink Payoff_matrix.
- Matching_pennies wikiPageWikiLink Penalty_kick.
- Matching_pennies wikiPageWikiLink Penny.
- Matching_pennies wikiPageWikiLink Pure_strategy.
- Matching_pennies wikiPageWikiLink Repeated_game.
- Matching_pennies wikiPageWikiLink Rock,_Paper,_Scissors.
- Matching_pennies wikiPageWikiLink Rock-paper-scissors.
- Matching_pennies wikiPageWikiLink Strategy_(game_theory).
- Matching_pennies wikiPageWikiLink Zero-sum_game.
- Matching_pennies wikiPageWikiLink File:Reaction-correspondence-matching-pennies.jpg.
- Matching_pennies wikiPageWikiLinkText "Matching pennies".
- Matching_pennies wikiPageWikiLinkText "matching pennies".
- Matching_pennies 1d "Tails".
- Matching_pennies 1u "Heads".
- Matching_pennies 2l "Heads".
- Matching_pennies 2r "Tails".
- Matching_pennies dl "−1, +1".
- Matching_pennies dr "+1, −1".
- Matching_pennies hasPhotoCollection Matching_pennies.
- Matching_pennies name "Matching pennies".
- Matching_pennies ul "+1, −1".
- Matching_pennies ur "−1, +1".
- Matching_pennies wikiPageUsesTemplate Template:About.
- Matching_pennies wikiPageUsesTemplate Template:Game_theory.
- Matching_pennies wikiPageUsesTemplate Template:Payoff_matrix.
- Matching_pennies subject Category:Game_theory.
- Matching_pennies hypernym Name.
- Matching_pennies comment "Matching pennies is the name for a simple example game used in game theory. It is the two strategy equivalent of Rock, Paper, Scissors. Matching pennies is used primarily to illustrate the concept of mixed strategies and a mixed strategy Nash equilibrium.The game is played between two players, Player A and Player B. Each player has a penny and must secretly turn the penny to heads or tails. The players then reveal their choices simultaneously.".
- Matching_pennies label "Matching pennies".
- Matching_pennies sameAs Unberechenbarkeit_(Spieltheorie).
- Matching_pennies sameAs سکههای_مطابق.
- Matching_pennies sameAs Matching_pennies.
- Matching_pennies sameAs m.04x9g9.
- Matching_pennies sameAs Q915573.
- Matching_pennies sameAs Q915573.
- Matching_pennies wasDerivedFrom Matching_pennies?oldid=609401147.
- Matching_pennies depiction Reaction-correspondence-matching-pennies.jpg.
- Matching_pennies isPrimaryTopicOf Matching_pennies.