Knowing What Others Know: Coordination Motives in Information Acquisition

Abstract

This section shows that the equilibrium of the action game in section 1 of the main text is unique.It does that by adapting an argument first made Angeletos and Pavan (2007, propositions 1 and 3) to our environment. The idea of the proof is that there is a social planner problem such that every equilibrium of our model is also a solution to this planning problem. The planning problem is strictly convex, meaning that it has a unique minimum. Since the planning problem has a unique solution and every equilibrium is a solution to the planning problem, the equilibrium of the model must be unique.We begin by setting up some notation for the proof. We letp (·) denote the candidate equilibrium function characterized by equation (4) in the main text, and will make use of the fact that s = b ω. We let F (ω) denote the prior distribution of ω, with density f (ω). We let µ denote the distribution of the agents' information choices, and φ (Xz|ω) the distribution of observed signals, conditional on the state ω. Together, µ and φ determine the distribution F (I|ω)of information sets I = (χ, Xz), conditional on the state ω. The agents' posterior beliefs conditional on I are defined by the pdfφ.Proposition 1 Let P denote the set of functions p for which

Exogenous Information, Endogenous Information, and Optimal Monetary Policy

“…Assuming that the central bank can commit to an interest rate rule of the form (11) instead of a money supply rule of the form (10) does not change optimal monetary policy. This is because the set of equilibria that the central bank can implement with an interest rate rule of the form (11) equals the set of equilibria that the central bank can implement with a money supply rule of the form (10). To see this, note the following.…”

“…Another example of a variable z t with the property ϕ > − φ z φ c is an aggregate technology shock or a labor supply shock in an economy with a positive production or consumption externality. take a law of motion of the economy that is an equilibrium law of motion under some interest rate rule of the form (11). One can then compute the equilibrium law of motion for the money supply from equation (44) and the central bank can commit to this law of motion as a money supply rule.…”

Cognitive Empathy in Conflict Situations

“…Market demand enters all agents' profit functions, whereas in our model the information a player might acquire is exclusively about the opponent's preferences. More general models in which players acquire information about an uncertain parameter affecting all players' preferences are given in Hellwig andVeldkamp (2009), Myatt andWallace (2012), and Amir and Lazzati (2014), as well as in Persico (2000) and Bergemann et al (2009) in a mechanism design context. Solan and Yariv (2004) consider a sequential model of two-player twoaction interaction in which one player chooses a (possibly mixed) action first, then a second player can buy, at some cost, information about the first player's (realized) action before finally then also choosing an action herself.…”

Beauty Contests and Irrational Exuberance: A Neoclassical Approach

“…(25) To see that this is indeed the case, note that, under any policy as in (12), the equilibrium price must satisfy p = K[9\K,uj} -tq -r p p -tkK. Equivalently, P = 1 + T" K,u>] -T -T K K (26) Next note that if the policy (to,t p ,tk-) implements the constrained efficient allocation, then (27) with coefficients (7o,7k,7w) as in Section 4 with (3q = 6$, Px = 5 X , and j3 y = 5 y , Replacing (27) into (26), one can then easily see that the policy with coefficients T = 70, tk = IK, r p = -y ul - 1. is such that p -6 -lu - 6 (34) Substituting (33) and (34) into (32) (36) into (35) …”