Matching Pennies

What are Matching Pennies?

Matching Pennies is an essential game theory model that shows how rational chiefs try to boost their payoffs. Matching Pennies includes two players all the while putting a penny on the table, with the payoff relying upon whether the pennies match. In the event that the two pennies are heads or tails, the principal player wins and keeps the other's penny; on the off chance that they don't match, the subsequent 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 every player has an equivalent likelihood of picking heads or tails and does as such at random, there is no Nash Equilibrium in this present circumstance; at the end of the day, neither one of the players has an incentive to try an alternate strategy.

Figuring out Matching Pennies

Matching Pennies is conceptually like the famous "Rock, Paper, Scissors," as well as the "chances and levels" game, where two players simultaneously show a couple of fingers and the not entirely set in stone by whether the fingers match.

Think about the accompanying guide to exhibit 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 arrangements of numerals displayed in the cells denoted (a) through (d), the primary numeral addresses Adam's payoff, while the subsequent entry addresses Bob's payoff. +1 means that the player wins a penny, while - 1 means that the player loses a penny.

On the off chance that Adam and Bob both play "Heads," the payoff is as displayed in cell (a) — Adam gets Bob's penny. On the off chance that Adam plays "Heads" and Bob plays "Tails," the payoff is switched; as displayed in cell (b), it would now be - 1, +1, and that means that Adam loses a penny and Bob gains a penny. In like manner, in the event that Adam plays "Tails" and Bob plays "Heads," the payoff as displayed in cell (c) is - 1, +1. On the off chance that both play "Tails," the payoff as displayed 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

A similar game can likewise be played with payoffs to the players that are not something very similar. Changing the payoffs additionally changes the optimal strategy for the players. For instance, in the event that each time the two players decide "Heads" Adam gets a nickel rather than a penny, then Adam has a greater expected payoff while playing "Heads" compared to "Tails."

Adam / Bob	Heads	Tails
Heads	(a) +5, -1	(b) -1, +1
Tails	(c) -1, +1	(d) +1, -1

To boost his expected payoff, Bob will presently pick "Tails" on a more regular basis. Since this is a zero-sum game, where Adam's gain is Bob's loss, by picking "Tails" Bob offsets Adam's greater payoff from a matching "Heads" outcome. Adam will keep on playing "Heads," since his greater payoff from matching "Heads" is currently offset by the greater likelihood that Bob will pick "Tails."

Features

A similar game can likewise be played with payoffs to the players that are not something very similar.
Matching Pennies is an essential game theory model that exhibits how rational chiefs look to boost their payoffs.
Matching Pennies is a zero-sum game in that one player's gain is the other's loss.