Matching Pennies

AAA

DEFINITION of 'Matching Pennies'

A basic game theory example that demonstrates how rational decision-makers seek to maximize their payoffs. “Matching Pennies” involves two players simultaneously placing a penny on the table, with the payoff depending on whether the pennies match. If both pennies are heads or tails, the first player wins and keeps the other’s penny; if they do not match, the second player wins and keeps the other’s penny. Matching Pennies is a zero-sum game in that one player’s gain is the other’s loss. Since each player has an equal probability of choosing heads or tails and does so at random, there is no “Nash Equilibrium” in this situation; in other words, neither player has an incentive to try a different strategy.

INVESTOPEDIA EXPLAINS 'Matching Pennies'

Matching Pennies is conceptually similar to the popular “Rock, Paper, Scissors,” as well as the “odds and evens” game where two players concurrently show one or two fingers and the winner is determined by whether the fingers match.

Consider the following example to demonstrate the Matching Pennies concept. Adam and Bob are the two players in this case, and the table below shows their payoff matrix. Of the four sets of numerals shown in the cells marked (a) through (d), the first numeral represents Adam’s payoff, while the second entry represents Bob’s payoff. +1 means that the player wins a penny, while -1 means that the player loses a penny.

If Adam and Bob both play “Heads,” the payoff is as shown in cell (a) – Adam gets Bob’s penny. If Adam plays “Heads” and Bob plays “Tails,” then the payoff is reversed; as shown in cell (b), it would now be -1, +1, which means that Adam loses a penny and Bob gains a penny. Likewise, if Adam plays “Tails” and Bob plays “Heads,” the payoff as shown in cell (c) is -1, +1, and if both play “Tails” the payoff as shown in cell (d) is +1, -1.

Adam  /   Bob

Heads

Tails

Heads

(a) +1, -1

(b) -1, +1

Tails

(c) -1, +1

(d) +1, -1

 

RELATED TERMS
  1. All-Pay Auction

    An economic and game theory concept in which participants place ...
  2. Decision Theory

    An interdisciplinary approach to determine how decisions are ...
  3. Shapley Value

    In game theory, a manner of fairly distributing both gains and ...
  4. Trembling Hand Perfect Equilibrium

    In game theory, an equilibrium state that takes into consideration ...
  5. Tit For Tat

    A game-theory mechanism which is subject to a payoff matrix similar ...
  6. Diner's Dilemma

    A game-theory situation with several players. Similar to a prisoner's ...
RELATED FAQS
  1. Why is Game Theory useful in business?

    Game theory was once hailed as a revolutionary interdisciplinary phenomenon bringing together psychology, mathematics, philosophy ... Read Full Answer >>
Related Articles
  1. Economics

    Economics Basics

    Learn economics principles such as the relationship of supply and demand, elasticity, utility, and more!
  2. Economics

    Macroeconomics

    Find out everything you need to know about macroeconomics.
  3. Economics

    Adam Smith: The Father Of Economics

    This free thinker promoted free trade at a time when governments controlled most commercial interests.
  4. Professionals

    A Day In The Life Of An Economist

    We've interviewed three economists with very different job descriptions to give you an idea of the many possibilities this career choice offers.
  5. Options & Futures

    Nobel Winners Are Economic Prizes

    Before you try to profit from their theories, you should learn about the creators themselves.
  6. Personal Finance

    The Economics Of A Successful Marriage

    These theories can keep multi-million dollar corporations afloat, so they should be able to increase the odds of wedded bliss.
  7. Personal Finance

    Microeconomics

    This tutorial teaches the basics of one of the most important economic topics. A must for all investors.
  8. Options & Futures

    Game Theory: Beyond The Basics

    Take your game theory knowledge to the next level by learning about simultaneous games and the Nash Equilibrium.
  9. Fundamental Analysis

    The Basics Of Game Theory

    Break down and examine the potential consequences of economic/financial scenarios.
  10. Chart Advisor

    4 Bullish Flag Patterns You Should Trade Now

    Here are four stocks with flag patterns, highlighting the various ways to trade this chart pattern.

You May Also Like

Hot Definitions
  1. Risk Averse

    A description of an investor who, when faced with two investments with a similar expected return (but different risks), will ...
  2. Fixed-Charge Coverage Ratio

    A ratio that indicates a firm's ability to satisfy fixed financing expenses, such as interest and leases. It is calculated ...
  3. Efficiency Ratio

    Ratios that are typically used to analyze how well a company uses its assets and liabilities internally. Efficiency Ratios ...
  4. Fixed Cost

    A cost that does not change with an increase or decrease in the amount of goods or services produced. Fixed costs are expenses ...
  5. Subsidy

    A benefit given by the government to groups or individuals usually in the form of a cash payment or tax reduction. The subsidy ...
  6. Sunk Cost

    A cost that has already been incurred and thus cannot be recovered. A sunk cost differs from other, future costs that a business ...
Trading Center