Imperfect-Recall Abstractions with Bounds in Games

Imperfect-recall abstraction has emerged as the leading paradigm for practical large-scale equilibrium computation in incomplete-information games. However, imperfect-recall abstractions are poorly understood, and only weak algorithm-specific guarantees on solution quality are known. In this paper, we show the first general, algorithm-agnostic, solution quality guarantees for Nash equilibria and approximate self-trembling equilibria computed in imperfect-recall abstractions, when implemented in the original (perfect-recall) game. Our results are for a class of games that generalizes the only previously known class of imperfect-recall abstractions where any results had been obtained. Further, our analysis is tighter in two ways, each of which can lead to an exponential reduction in the solution quality error bound. We then show that for extensive-form games that satisfy certain properties, the problem of computing a bound-minimizing abstraction for a single level of the game reduces to a clustering problem, where the increase in our bound is the distance function. This reduction leads to the first imperfect-recall abstraction algorithm with solution quality bounds. We proceed to show a divide in the class of abstraction problems. If payoffs are at the same scale at all information sets considered for abstraction, the input forms a metric space. Conversely, if this condition is not satisfied, we show that the input does not form a metric space. Finally, we use these results to experimentally investigate the quality of our bound for single-level abstraction

Profitability of Horizontal Mergers in Trigger Strategy Game

It is shown that, in a dynamic competition, an exogenous horizontal merger is profitable even if a small share of active firms merge. However, each firm has incentive to remain outside the merger because it would benefit more (Insiders’dilemma). We show that in an infinite repeated game in which the firms use trigger strategies an exogenous bilateral merger can be profitable and the Insiders’dilemma is mitigated.Horizontal mergers; Insiders’ dilemma; trigger strategy

Possibilistic Boolean games: strategic reasoning under incomplete information

Boolean games offer a compact alternative to normal-form games, by encoding the goal of each agent as a propositional formula. In this paper, we show how this framework can be naturally extended to model situations in which agents are uncertain about other agents' goals. We first use uncertainty measures from possibility theory to semantically define (solution concepts to) Boolean games with incomplete information. Then we present a syntactic characterization of these semantics, which can readily be implemented, and we characterize the computational complexity

Non-neutrality of economic policy: An application of the Tinbergen-Theil’s approach to a strategic context

Issues of policy effectiveness and neutrality are widespread in the economic literature. They have been increasingly raised in specific contexts within the class of LQ (linear-quadratic) policy games in the last 20 years, notably with reference to monetary policy. The more general conditions ensuring nonneutrality in a strategic environment remain however to be inquired. We fill this gap by applying the classical theory of economic policy to a strategic context. This is also useful to highlight some existence conditions for policy game solutions. We restrict ourselves to the common LQ-games in a static perfect information framework, but our simple logic can be extended to other more general situations.LQ-policy games, policy ineffectiveness, controllability.

The Profitability of Small Horizontal Mergers with Nonlinear Demand Functions

We want to take a differential game approach with price dynamics to conduct an investigation into the consequences of horizontal merger of firms where the demand function is nonlinear. We take into consideration the open-loop equilibrium. We show that in relation to the fact that the demand is nonlinear and prices follow some stickiness an incentive for small merger exists, while it does not appear under the standard approach using a linear demand function.

No advantageous merging in minimum cost spanning tree problems

In the context of cost sharing in minimum cost spanning tree problems, we introduce a property called No Advantageous Merging. This property implies that no group of agents can be better off claiming to be a single node. We show that the sharing rule that assigns to each agent his own connection cost (the Bird rule) satisfies this property. Moreover, we provide a characterization of the Bird rule using No Advantageous Merging.Minimum cost spanning tree problems; cost sharing; Bird rule; No Advantageous Merging