Question

3. In simultaneous game, please set up a game where there is more than one Nash equilibrium and please use the mixed strategy to solve the focal point equilibrium of the game. (10 points)

Answer 1

Let's consider 2 rival companies of "Procter & Gamble" and "Unilever". The payoff's on advertising and on not advertising are as below-

Unilever Advertise Don't Advertise PnG Don't advertise 5,5 1, 10 Advertise 10,1 3,3

¡Decision to advertise is SIMULTANEOUS and INDEPENDENT.

¡Advertising is a dominant strategy for both firms

§Payoff from advertising is higher than from not advertising regardless of what opponent does

¡Payoff from both advertising is lower than from both not advertising

§Individual self interest can lead to both becoming worse off!

§This is an another example of Prisoner’s dilemma

In the above scenario, there are 2 nash equilibrium's at (5,5) and (3,3) where both are not advertising or both are advertising.

Considering your dominant strategy, you would want to advertise and your rival to not advertise for maximum gain.

However, in such cases, we are to expect our rivals to play their dominant strategy.

Unilever Advertise Don't Advertise PnG Don't advertise 5,5 1, 10 Advertise 10,1 0,3

¡PnG does not have a dominant strategy

¡Unilever has a dominant strategy

§It will advertise no matter what PnG does

¡Expecting this, PnG will choose not to advertise

Thus, the simultaenous game of advertising is set up with more than one Nash equilibrium and we used the mixed strategy (not just considering our outcomes but considering the outcome of rivals for taking our decision) to solve the focal point equilibrium of the game.