What are Matching Pennies?
Matching Pennies is a basic recreation idea example that demonstrates how rational decision-makers seek to maximize their payoffs. Matching Pennies comes to 2 avid players at the same time as striking a penny on the table, with the payoff depending on whether or not or no longer the pennies are compatible. If every pennies are heads or tails, the principle player wins and assists in keeping the other’s penny; if they do not are compatible, the second player wins and assists in keeping the other’s penny. Matching Pennies is a zero-sum recreation in that one player’s gain is the other’s loss. Since each player has an similar probability of choosing heads or tails and does so at random, there is no Nash Equilibrium in this situation; in numerous words, neither player has an incentive to take a look at a novel method.
Key Takeaways
- Matching Pennies is a basic recreation idea example that demonstrates how rational decision-makers seek to maximize their payoffs.
- Matching Pennies is a zero-sum recreation in that one player’s gain is the other’s loss.
- The equivalent recreation can also be carried out with payoffs to the avid players that aren’t the equivalent.
Figuring out Matching Pennies
Matching Pennies is conceptually similar to the most popular “Rock, Paper, Scissors,” along with the “odds and evens” recreation, where two avid players similtaneously show one or two fingers and the winner is determined by means of whether or not or no longer the fingers are compatible.
Believe the following example to expose the Matching Pennies concept. Adam and Bob are the two avid players in this case, and the table below displays their payoff matrix. Of the 4 devices of numerals confirmed inside the cells marked (a) via (d), the principle numeral represents Adam’s payoff, while the second get right of entry to 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 every play “Heads,” the payoff is as confirmed in cell (a)—Adam gets Bob’s penny. If Adam plays “Heads” and Bob plays “Tails,” then the payoff is reversed; as confirmed in cell (b), it is going to now be -1, +1, this means that that that Adam loses a penny and Bob just right issues a penny. Likewise, if Adam plays “Tails” and Bob plays “Heads,” the payoff as confirmed in cell (c) is -1, +1. If every play “Tails,” the payoff as confirmed in cell (d) is +1, -1.
|
Adam / Bob |
Heads |
Tails |
|
Heads |
(a) +1, -1 |
(b) -1, +1 |
|
Tails |
(c) -1, +1 |
(d) +1, -1 |
Asymmetric Payoffs
The equivalent recreation can also be carried out with payoffs to the avid players that aren’t the equivalent. Changing the payoffs moreover changes the optimal method for the avid players. For example, if every time every avid players make a selection “Heads” Adam receives a nickel as a substitute of a penny, then Adam has a greater expected payoff when playing “Heads” compared to “Tails.”
|
Adam / Bob |
Heads |
Tails |
|
Heads |
(a) +5, -1 |
(b) -1, +1 |
|
Tails |
(c) -1, +1 |
(d) +1, -1 |
In order to maximize his expected payoff, Bob will now make a selection “Tails” further forever. On account of it is a zero-sum recreation, where Adam’s gain is Bob’s loss, by means of choosing “Tails” Bob offsets Adam’s upper payoff from an similar “Heads” result. Adam will continue to play “Heads,” because of his upper payoff from matching “Heads” is now offset by means of the upper probability that Bob will make a selection “Tails.”
