Simultaneous Games, Dominant and Dominated Strategies, Nash Equilibrium, Prisoner's Dilemma

1-2 Simultaneous Games I - Game Setting

A working definition of a strategy is a player's plan of actions in a game.
Simultaneous games as represented in a matrix structure.
The elements of a simultaneous games matrix are:

• Players e.g. Sensodyne, Colgate
• Actions e.g. Advertise, Don't Advertise
• Rules e.g. Simultaneous decisions
• Payoffs e.g.80% of market if advertise

1-3 Simultaneous Games II - Eliminating Dominated Strategies

A dominant strategy is a strategy that always does better than any other strategy regardless of what the other firm does.

• A rational player always chooses the dominant strategy. 
• We can anticipate that our rival will also choose the dominant strategy

A dominated strategy is a strategy that never does better than another one.

• A rational player would never opt for this strategy. 
• More importantly, you can rely on a rational rival never playing a dominated strategy

To solve this game, eliminate dominated strategies iteratively to eventually find the optimal strategy for each player.

1-4 Simultaneous Games III - Nash Equilibrium

A Nash Equilibirum is a combination of strategies such that any player that deviates from that equilibrium will have a worse payoff.
A good question to ask is: Does any player have an incentive to change their strategy?

Questions:

1. Is a Nash Equilibrium the same as a dominant strategy?
2. Can a Nash Equilibrium contain dominated strategies?
3. Will every Nash Equilibrium contain dominant strategies?
4. Will every game will have a Nash Equilibrium?
5. Can a game have more than one Nash Equilibrium?

1-5 Simultaneous Games IV - Prisoner's Dilemma

The Prisoner's Dilemma is a special form of Nash Equilibrium such that:

• there exists a combination of strategies with higher joint payoffs 
• but it is unlikely to be chosen because each player chooses a dominant strategy 
• and players gravitate to the lower-paying Nash Equilibrium