From Psychology Wiki

Community portal · Tasks to do · News · Help

Clinical · Educational · Ind&Org · Other fields · Professional · Transpersonal · World

Assessment | Biopsychology | Comparative | Cognitive | Developmental | Language | Personality | Philosophy | Research Methods | Social | Statistics

Statistics: Scientific method · Research methods · Experimental design · Undergraduate statistics courses · Statistical tests · Game theory · Decision theory

---

	Heads	Tails
Heads	+1, -1	-1, +1
Tails	-1, +1	+1, -1
Matching pennies

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, also called the Pesky Little Brother Game or Parity Game, 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 receives one dollar from Player B (+1 for A, -1 for B). If the pennies do not match (one heads and one tails), Player B receives one dollar 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 to the 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. Alternatively, there is no strategy set where neither player would want to switch when 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.

Of course, most human players cannot or will 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 against an opponent who plays the equilibrium, one's expected payoff is zero.

The matching pennies game is mathematically equivalent to a game children play called "choosing" 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. The only strategy for both these games to avoid being exploited is to perfectly randomize your selection.

[edit] References

• GameTheory.net

This box: view • talk • edit	Topics in game theory
Definitions	Normal form game · Extensive form game · Cooperative game · Information set · Preference
Equilibrium concepts	Nash equilibrium · Subgame perfection · Bayes-Nash · Trembling hand · Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · Evolutionarily stable strategy
Strategies	Dominant strategies · Mixed strategy · Grim trigger · Tit for tat
Classes of games	Symmetric game · Perfect information · Dynamic game · Repeated game · Signaling game · Cheap talk · Zero-sum game · Mechanism design
Games	Prisoner's dilemma · Coordination game · Chicken · Battle of the sexes · Stag hunt · Matching pennies · Ultimatum game · Minority game · Rock, Paper, Scissors · Pirate game · Dictator game · Public goods game
Theorems	Minimax theorem · Purification theorems · Folk theorem · Revelation principle · Arrow's Theorem
Related topics	Mathematics · Economics · Behavioral economics · Evolutionary game theory · Population genetics · Behavioral ecology · Adaptive dynamics · List of game theorists

This page uses content from the English-language version of Wikipedia. The original article was at Matching Pennies. The list of authors can be seen in the page history. As with Psychology Wiki, the text of Wikipedia is available under the GNU Free Documentation License.