Question

California and Nevada are adopting electronic medical records (EMR) systems, provided by either Kareo or Praxis. Each state has a preference for using one of these systems rather than the other, but all else equal, both states would like to use the same system since doing so makes it easier to coordinate healthcare for people who commute across state lines.

3 Coordinated care (9 pts.) California and Nevada are adopting electronic medical records (EMR) systems, provided by either Kareo or Praxis. Each state has a preference for using one of these systems rather than the other, but all else equal, both states would like to use the same system since doing so makes it easier to coordinate healthcare for people who commute across state lines. Nevada Kareo Praxis 6,1 0,0 0,0 3,5 California Kareo Praxis a. (1 pt.) What is California's best response against Nevada choosing Praxis? b. (2 pts.) Identify any/all pure strategy Nash equilibria (in each case, list the strategies as an ordered pair). For each PSNE, also indicate the corresponding equilibrium payoffs. c. (3 pts.) Suppose that California picks Kareo with probability and that Nevada picks Kareo with probability . Show that this cannot be a mixed strategy Nash equilibrium. Which player is not playing a best response? d. (3 pts. Now imagine that California makes its decision first. California's decision will be public knowledge, so Nevada will get to see what California did before making its decision. Draw the game tree corresponding to this dynamic game. What will California do? How will Nevada respond? What are the equilibrium payoffs?

Answer 1

Solution: Given the payoffs from the available choices (of using one of the EMR systems rather than the other) for two states California and Nevada, we have a 2×2 game as follows;

California	Nevada
		Kareo	Praxis
	Kareo	6,1	0,0
	Praxis	0,0	3,5

1. California’s Best response against Nevada choosing Praxis would be California choosing Praxis as well which will give them a payoff of (3,5).
2. A pure strategy Nash Equilibrium (NE) is that in which the probability of choosing a particular strategy is 1 for each state. There are two pure strategies NE such as (Kareo, Kareo) and (Praxis, Praxis). Because any state considering to opt for a different EMR system while the other state is sticking to a particular choice of EMR system would be worse off. Thus, we have two NE here such as the ordered pairs (Kareo, Kareo) and (Praxis, Praxis); and their respective payoff are (6,1) and (3,5) respectively.
3. Given that California picks Kareo with Probability 3/4 and Nevada picks Kareo with probability 1/3. Then we know that California picks Praxis with Probability 1/4 and Nevada picks Praxis with probability 2/3.

Given Nevada’s mixed strategy (1/3,2/3), California’s expected payoff’s to pure strategy Kareo is given by;     6*(1/3)+0*(2/3)=2

Given Nevada’s mixed strategy (1/3,2/3), California’s expected payoff’s to pure strategy Praxis is given by;     0*(1/3)+3*(2/3)=2

Given California’s mixed strategy (3/4, 1/4), Nevada’s expected payoff’s to pure strategy Kareo is given by;     1*(3/4) + 0*(1/4) = 3/4

Given California’s mixed strategy (3/4, 1/4), Nevada’s expected payoff’s to pure strategy Praxis is given by;     0*(3/4) + 5*(1/4) = 5/4.

Thus, as we saw from above that Nevada is not indifferent between Kareo and Praxis against California’s mixed strategy (3/4, 1/4). So, there is no mixed strategy NE. Also, as we saw California is indifferent to choose its best response.

See image attached for solution sub-part (d)

Solution : As california makes its first decision, the game tree looks like the following Figueres Nevada Kareo (61) ada kan Kako Californian hasis (0,0) forero Kareo Kareo - coo) * Nevada Precarie (35) Here, the equilibeiiem payoffs would be (6, 1) and (3,5). Anyone state deviating from this order paid would be worse off. Thas no body has any tendency of deviating from til egil' boliem state.