Characterising equilibrium selection in global games with strategic complementarities

Abstract

Abstract. Global games are widely used for equilibrium selection to predict behaviour in complete information games with strategic complementarities. We establish two results on the global game selection. First, we show that it is independent of the payoff functions of the global game embedding, though it may depend on the noise distribution. Second, we give a simple sufficient criterion for noise independence in many action games. A many action game may be noise independent if it can be suitably decomposed into smaller (say, binary action) games, for which there are simple criteria guaranteeing noise independence. We delineate the games where noise independence may be established by counting the number of players or actions. In addition, we give an elementary proof that robustness to incomplete information implies noise independence.

Crossing network versus dealer market: Unique equilibrium in the allocation of order flow

“…Since the number Due to strategic complements, andŨ k being monotonic in θ, a best reply iteration in e starting from y must lead upwards and converge to some equilibrium where y(x) ≥ a nν (η * * ) for some x. By Theorem 2 in [2], this implies a n ≥ a nν (η * * ), and we know a nν (η * * ) ≥ a nν (η * ). Thus, our claim is proved.…”

“…If the CN attracts sufficient liquidity, no trader has an incentive to leave the CN. Of these two equilibria, coordination on the CN is the Pareto efficient equilibrium, because it maximises expected payoff: π(θ − t cn ) ≥ (θ − t dm ), where the inequality follows from (2).…”

“…Hence, the thicker a market, the higher is the liquidity preference at which traders are indifferent in equilibrium. For λ → ∞, the probability of order execution π(α) approaches ln (2) for all α > 0. From Propositions 5 and 8 we now readily deduce:…”

“…We will prove this using methods in Basteck, Daniëls and Heinemann [2]. Since, for each ν, a ν (η) converges to a(η) for each η, and for each ν, a ν is a profile of increasing functions taking on only finitely many values, there is some ν > 0 such that, for all 0 < ν ≤ ν, and all η in a 8νm-neighbourhood of η * , a ν (η) = a(η * ).…”

“…Compared with the global game Γ n , the distribution of individual signals remains unchanged. We assume an improper uniform prior, so the posterior beliefs in e are well defined and take the same form as in [2] and in Γ n .…”