Q5E Two major networks are competing... [FREE SOLUTION]

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Chapter 13: Q5E (page 501)

Two major networks are competing for viewer ratings in the 8:00鈥�9:00 p.m. and 9:00鈥�10:00 p.m. slots on a given weeknight. Each has two shows to fill these time periods and is juggling its lineup. Each can choose to put its 鈥渂igger鈥� show first or to place it second in the 9:00鈥�10:00 p.m. slot. The combination of decisions leads to the following 鈥渞atings points鈥� results:
a. Find the Nash equilibria for this game, assuming that both networks make their decisions at the same time.
b. If each network is risk-averse and uses a maximin strategy, what will be the resulting equilibrium?
c. What will be the equilibrium if Network 1 makes its selection first? If Network 2 goes first?
d. Suppose the network managers meet to coordinate schedules and Network 1 promises to schedule its big show first. Is this promise credible? What would be the likely outcome?

Short Answer

Expert verified

Nash equilibrium will be obtained when Network 1 and Network 2 air the bigger show first and receive payoffs 20 and 30, respectively.
If the networks resort to a minimax approach, the resulting equilibrium is (First, First) with the corresponding payoff of (20, 30).
Even if the game is played sequentially instead of simultaneously, the equilibrium will remain the same as the Nash equilibrium.
Network 1鈥檚 promise is credible with the likely outcome of the networks operating at the Nash equilibrium.

Step by step solution

Computing the Nash equilibria during a simultaneous game

If Network 1 decides to place the bigger show first, Network 2 would also do the same and obtain ratings higher than obtained by placing the show second (30 > 18).
If Network 1 decides to place the bigger show second, Network 2 will air it first to obtain ratings higher than obtained by placing the show second (15 > 10).

Thus, Network 2 has a dominant strategy of placing the bigger show first irrespective of Network 1鈥檚 decision.

If Network 2 airs the bigger show first, Network 1 would also do the same and obtain ratings higher than obtained by placing the show second (20 > 15).
If Network 2 airs the bigger show second, Network 1 will air it second to obtain ratings higher than obtained by airing it first (30 > 18).

Thus, Network 1 does not have a clear dominant strategy.

However, as Network 2 has the dominant strategy of airing the bigger show first and would do so irrespective of Network 1鈥檚 strategy, Network 1 would also place the bigger show first to get a higher rating of 20.

Thus, the Nash equilibrium will be obtained when Network 1 and Network 2 air the bigger show first and receive ratings 20 and 30, respectively.

Computing the strategy of risk-averse networks

When the networks are risk-averse and wish to apply the maximin approach to determine their strategies, they aim to minimize the adverse outcomes of the game.

If Network 1 opts for First, the least ratings it will get is 18. If it opts for Second, the least ratings it will get is 15. Thus, the network can minimize low ratings by opting for First.

Similarly, if Network 2 opts for First, the least ratings it will get is 15. If it opts for Second, the least ratings it will get is 10. Thus, the network can minimize low ratings by opting for First.

As both networks opt for First, the resulting equilibrium is (First, First) with the corresponding payoff of (20, 30).This equilibrium is the same as the Nash equilibrium previously obtained.

Equilibrium of the firms if they follow a sequential game

If the networks follow a sequential game, one network鈥檚 decision will impact the other. We have obtained that Network 2 has a dominant strategy and will choose First regardless of Network 1鈥檚 strategy.

As Network 1 makes its selection first, it can maximize its payoff by airing the bigger show first. Thus, the equilibrium will be attained at the point (First, First), the same as the Nash equilibrium. The outcome remains the same if Network 2 makes the selection first.

Even if the game is played sequentially instead of simultaneously, the equilibrium will remain the same as the Nash equilibrium.

Assessing the credibility and outcome of Network 1’s promise

Network 1 makes a promise of scheduling the bigger show first. The commitment will be credible only if Network 1 is not incentivized to behave otherwise.

The Nash equilibrium computed in part (a) states the optimal strategy of Network 1 to schedule the bigger show first. As none of the networks has any incentive to diverge from the Nash equilibrium, Network 1鈥檚 promise is credible.

Thus, Network 1 schedules the bigger show first due to the credibility of its promise, and the equilibrium is attained at (First, First) with the firms earning the payoff (20, 30).