15.5 Exercis 317 3,3.2)(0,0,0)(4,4,0 FIGURE 15.6 Selten\'s honse, exercise 15.6

Question

15.5 Exercis 317 3,3.2)(0,0,0)(4,4,0 FIGURE 15.6 Selten's honse, exercise 15.6 Exiting costs nothing to the entrant. The entrant knows his type, but the incumbent knows only the prior distribution: Pr In response to any level of entry, the incumbent can modate (A) or fight (F). Accommodating an entrant imposes no costs. Inde- rendent of the entrant's type, accommodating small entry gives the incumbent 60% of the market and the entrant 40%, while accommodating big entry gives incumbent 40% of the market and the entrant 60%. Fighting a tough entrant the incumbent's market share by 20% (relative to accommodating) but imposes a cost of 4 on the incumbent. Fighting a weak entrant that chose s increases the market share of the incumbent to 10% hut m poses acost of 2 on the incumbent. Fighting a weak entrant that chose B increases the market share of the incumbent to 100% but imposes a cost of 8 on the incumbent. Draw this game in extensive form. Using a matrix representation, find all the pure-strategy Bayesian Nash equilibria for this game. Which one of the Bayesian Nash equilibria is preferred by the incum- bent? Can it be supported as a perfect Bayesian equilibrium? Find all the perfect Bayesian equilibria of this game. a. b. c. d. 56 Selten's Horse: Consider the three-person game described in Figure 15.6, known as Selten's horse (for the obvious reason). a. What are the pure-strategy Bayesian Nash equilibria of this game? b. Which of the Bayesian Nash equilibria that you found in (a) are perfect Which of the Bayesian Nash equilibria that you found in (a) are sequential equilibria? Bayesian equilibria? c.

Explanation / Answer

1). Pure strategy Nash equilibrium:

It can be verified that there are two pure strategy Nash equilibria.

(B, D, and F) and (A, D, E)

2). Perfect Bayesian equilibria:

Perfect Bayesian Equilibrium is a relatively weak equilibrium concept for dynamic games of incomplete information. It is often strengthened by restricting beliefs of information sets that are not reached along the equilibrium path.

Therefore, there is a unique pure strategy Perfect Bayesian Equilibrium outcome

(B, D, and F)

The belief system that supports this could be any µ (left) [0, 1/3].

3). Sequential Equilibria:

However, if we look at sequential rationality, the second of these equilibria (B, D, and F) and (A, D, E) will be ruled out.

Suppose we have (A, D, E)

The belief of player 3 will be µ3 (left) = 1.

Player 2, if he gets a chance to play, will then never play D, since C has a payoff of 4, while D would give him 1. If he were to play C, then player of 1 would prefer B, but (B, C, E) is not an equilibrium, because then we would have µ3 (left) = 0 and player 3 would prefer F.

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.