Question

Write about a game one can experience in their everyday life. Describe who the players are, what moves are available to them, what information they have when moving, and why the payoffs are what they are.

Draw out a game tree. How many strategies do the players have? What are they?

Are there any pure strategy Nash equilibria? If so, does the game usually turn out that one of them was played? If so, which one? Why do you think this is the case?

Answer 1

Matching Pennies is one of the best examples of the application Game theory in daily life. Most of us either know or played this interesting game. This game teaches how a decision maker can maximise his payoffs thinking rationally. Matching penny include two players, they place penny on the table together. Their payoff depends on whether the penny matches or not. Both players know the possible moves and its consequences as they know the rules of the game. If both pennies are heads and tails, the player who played first wins and keeps other’s pennies with him. In other way, if both pennies do not match, the second player wins and keeps first player’s penny. Matching pennies is considered as a zero-sum game, because one player’s win is treated as the other player’s loss. Each player has an equal chance to select heads or tails, they do it randomly. Therefore, there is no nash equilibrium in this situation, because neither player has not encouraged to select different strategy to beat his counter player’s move.

Following figure shows the matching pennies payoff matrix of two players A and B.

A/B	Heads	Tails
Heads	+1,-1	ii) -1, +1
Tails	iii) -1, +1	iv) +1, -1

  

The table shows the payoff numbers of both players A, B, the first number represents payoffs of player A and second number shows payoffs of player B. +1 means, player wins a penny and -1 is losing a penny. If both players play “Heads” first player wins that’s why in (i), player A got +1 and player B got -1. Here player A got B’s pennies. If A plays “Heads” B plays “Tails”, reverse is happened. Therefore, in cell (ii) it is (-1,+1), meaning is A losses a penny and B gain A’s penny. Similarly, if player A plays “Tails” and B plays “Heads”, the payoffs will be like in cell (iii) and if both play “Tails” player A wins B’s penny as shown in cell (iv).