Rational Players in Games (2)

There are reasons why we choose action or don’t choose on that action. Considering follows rational options:

• Dominance: A strategy dominates another strategy of a player if it always gives a better payoff to that player, regardless of what the other players are doing. It weakly dominates the other strategy if it is always at least as good. 
• Equilibrium: A Nash equilibrium, also called strategic equilibrium, is a list of strategies, one for each player which has the property that no player can unilaterally change his strategy and get a better payoff. Example: Prisoner’s Dilemma This Prisoner’s Dilemma is a game in strategic form between two players. Each player has two strategies called “cooperate” and “defect”, which are labeled C and D for player I and c and d for player II, respectively, as following figure.

 

This figure also shows payoff of each player. Player I chooses a row, either C or D, and player II chooses column, either c or d. The strategy combination (C, c) has payoff (2, 2) means each player has payoff 2. The strategy combination (C, d) has payoff (0, 3), means player I get payoff 2 and player II has payoff 3. The combination (D,c) results in payoff 3 for player I and 0 for player II. The combination (D,d) is played, player I and player II get 1.

Rational player of this game is finding dominance and equilibrium. For dominance, player I has the D strategy dominating another strategy because payoff of D is better C if player II chooses c and payoff D is also better C if player II chooses d. In the same way strategy d dominates c for player II. Later rational equilibrium of players, each player don’t choose dominated strategy, since then both choose (D,d) that is the equilibrium, even if they don’t desire.