1 bb.csueastbay.edu 2. Consider the following entry or exit game. Recall that, i
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1 bb.csueastbay.edu 2. Consider the following entry or exit game. Recall that, if X is a random variable as payouts are here, then the expected value of X is just the sum of the possible outcomes where each is weighted by the probability that it happens. Assume that for any pair of strategies for the new and old cleaner there is a 70% chance the economy is normal and a 30% chance there is a recession. Payouts are in the order (New Cleaner, Old Cleaner). 1 of 2 a) Solve for the Subgame Perfect Nash Equilibrium of this sequential game. b) Suppose the order of play is reversed, i.e. the Old Cleaner first sets a price, then the New Cleaner makes an entrance decision, and then we learn if we are in a recession or not and what our payoffs are. Solve for the Nash Equilibrium now. Can the Old Cleaner deter market entry in this case? What about in the first case?Explanation / Answer
a)
Consider the case where New Cleaner decides to Enter.
The expected payoff to Old Cleaner from setting High Price is = (0.7*100) + (0.3*-40) =70-12=58
The expected payoff to Old Cleaner from setting Low Price is = (0.7*-50) + (0.3*100) =-35+30=-5
Hence the Old Cleaner will set a high price when the New Cleaner decides to Enter.
The expected payoff to New Cleaner from Enter is = (0.7*100) + (0.3*40) =70+12=82
Consider the case where New Cleaner decides to Stay Out.
The expected payoff to Old Cleaner from setting High Price is = (0.7*300) + (0.3*240) =210+72=282
The expected payoff to Old Cleaner from setting Low Price is = (0.7*50) + (0.3*100) =35+30=65
Hence the Old Cleaner will set a high price when the New Cleaner decides to Stay Out.
The expected payoff to New Cleaner from Stay Out is = (0.7*0) + (0.3*0) =0
Therefore the New Cleaner will decide to Enter.
The Sub-game perfect equilibrium of the game is {Enter, High Price} where New Cleaner Enters the market and the Old Cleaner sets a High Price.
b)
Consider the case where Old Cleaner sets the High price.
Expected payoff to new cleaner from choosing Enter = (0.7*100)+(0.3*40) = 70+12=82
Expected payoff to new cleaner from choosing Stay Out = (0.7*0)+(0.3*0) = 0
Hence the New Cleaner will Enter when the Old Cleaner sets a High Price.
Expected payoff for Old Cleaner = (0.7*100) + (0.3*-40) =70-12=58
Consider the case where Old Cleaner sets the Low price.
Expected payoff to new cleaner from choosing Enter = (0.7*-100)+(0.3*20) = -70+6=-64
Expected payoff to new cleaner from choosing Stay Out = (0.7*0)+(0.3*0) = 0
Hence the New Cleaner will Stay Out when the Old Cleaner sets a Low price.
Expected payoff for Old Cleaner = (0.7*50) + (0.3*100) =35+30=65
Here we can see that the sub-game perfect equilibrium is {Low Price, Stay Out} where Old Cleaner sets a Low price and New Cleaner stays out.
Therefore here, the Old cleaner can deter entry by charging a low price. In the first case, the old cleaner could not deter entry as the New cleaner would have entered irrespective of the price charged by the Old cleaner.
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