Symmetric Subgame-Perfect Equilibria in Resource Allocation

We analyze symmetric protocols to rationally coordinate on an asymmetric, efficient allocation in an infinitely repeated N-agent, C-resource allocation problems, where the resources are all homogeneous. Bhaskar proposed one way to achieve this in 2-agent, 1-resource games: Agents start by symmetrically randomizing their actions, and as soon as they each choose different actions, they start to follow a potentially asymmetric "convention" that prescribes their actions from then on. We extend the concept of convention to the general case of infinitely repeated resource allocation games with N agents and C resources. We show that for any convention, there exists a symmetric subgame-perfect equilibrium which implements it. We present two conventions: bourgeois, where agents stick to the first allocation; and market, where agents pay for the use of resources, and observe a global coordination signal which allows them to alternate between different allocations. We define price of anonymity of a convention as a ratio between the maximum social payoff of any (asymmetric) strategy profile and the expected social payoff of the subgame-perfect equilibrium which implements the convention. We show that while the price of anonymity of the bourgeois convention is infinite, the market convention decreases this price by reducing the conflict between the agents

The Inefficiency of Nash and Subgame Perfect Equilibria for Network Routing

This paper provides new bounds on the quality of equilibria in finite congestion games with affine cost functions, specifically for atomic network routing games. It is well known that the price of anarchy equals exactly 5/2 in general. For symmetric network routing games, it is at most (5n−2)/(2n+ 1), where n is the number of players. The paper answers to two open questions for congestion games. First, we show that the price of anarchy bound (5n−2)/(2n+ 1) is tight for symmetric network routing games, thereby answering a decade-old open question. Secondly, we ask if sequential play and subgame perfection allows to evade worst-case Nash equilibria, and thereby reduces the price of anarchy. This is motivated by positive results for congestion games with a small number of players, as well as recent results for other resource allocation problems. Our main result is the perhaps surprising proof that subgame perfect equilibria of sequential symmetric network routing games with linear cost functions can have an unbounded price of anarchy. We complete the picture by analyzing the case with two players: We show that the sequential price of anarchy equals 7/5, and that computing the outcome of a subgame perfect equilibrium is NP-hard

On the equilibrium concept for overlapping generations organizations

A necessary feature for equilibrium is that beliefs about the behavior of other agents are rational. We argue that in stationary OLG environments this implies that any future generation in the same situation as the initial generation must do as well as the initial generation did in that situation. We conclude that the existing equilibrium concepts in the literature do not satisfy this condition. We then propose an alternative equilibrium concept, organizational equilibrium, that satisfies this condition. We show that equilibrium exists, it is unique, and it improves over autarky without achieving optimality. Moreover, the equilibrium can be readily found by solving a maximization program.Economics ; Equilibrium (Economics) - Mathematical models

Low Price Equilibrium in Multi-Unit Auctions: The GSM Spectrum Auction in Germany

The second-generation GSM spectrum auction in Germany is probably the most clear cut example of a low price outcome in a simultaneous ascending-bid auction.The present paper gives an account of the events, describes the auction rules and market conditions, and provides a theoretical explanation of low price equilibria in simultaneous, ascending-bid auctions.In particular it is shown that the low price equilibrium that implements the efficient allocation is the unique perfect equilibrium of that game.Multi-unit auctions, spectrum auctions, telecomm-unications, industrial organization, game theory

Endogenous Political Economy: On the Inevitability of Inefficiency under the Natural Resource Curse

This paper is a first step toward a more fundamental theory of political economy outcomes. We start from the fundamentals of the economy, given by preferences and technology; further, we specify all available technologies for the control of resources - such as armed forces or bribing. We model the interaction of agents in this economy as a game and examine all its equilibria. Equilibrium allocations must be such that individuals maximize their utility and that no group of individuals has the incentive to modify those allocations by (additional) usage of the technologies for the control of resources. The generality of our approach enables us to answer the question "Is there something about the nature of a country that makes inefficient equilibria inevitable?" We illustrate our approach by applying it to the natural resource curse. The model predicts that inefficient outcomes - in the form of either conflict or a deterrence army solution - will always occur as long as the value of natural resources to capture is positive and the opportunity cost of time - which partly determines soldiers' wages - is finite.Endogenous political economy; conflict; deterrence; natural resource curse; inefficiency; general equilibrium

Applications of Repeated Games in Wireless Networks: A Survey

A repeated game is an effective tool to model interactions and conflicts for players aiming to achieve their objectives in a long-term basis. Contrary to static noncooperative games that model an interaction among players in only one period, in repeated games, interactions of players repeat for multiple periods; and thus the players become aware of other players' past behaviors and their future benefits, and will adapt their behavior accordingly. In wireless networks, conflicts among wireless nodes can lead to selfish behaviors, resulting in poor network performances and detrimental individual payoffs. In this paper, we survey the applications of repeated games in different wireless networks. The main goal is to demonstrate the use of repeated games to encourage wireless nodes to cooperate, thereby improving network performances and avoiding network disruption due to selfish behaviors. Furthermore, various problems in wireless networks and variations of repeated game models together with the corresponding solutions are discussed in this survey. Finally, we outline some open issues and future research directions.Comment: 32 pages, 15 figures, 5 tables, 168 reference

Forward Trading in Exhaustible-Resource Oligopoly

We analyze oligopolistic exhaustible-resource depletion when firms can trade forward contracts on deliveries, a market structure prevalent in many resource commodity markets. We find that this organization of trade has substantial implications for resource depletion. As firms’ interactions become infinitely frequent, resource stocks become fully contracted and the symmetric oligopolistic equilibrium converges to the perfectly competitive Hotelling (1931) outcome. Asymmetries in stock holdings allow firms to partially escape the procompetitive effect of contracting: a large stock provides commitment to leave a fraction of the stock uncontracted. In contrast, a small stock provides commitment to sell early, during the most profitable part of the equilibrium.Forward trading, exhaustible resources, oligopoly pricing

Self-enforcing Agreements on Water allocation

Many water allocation agreements in transboundary river basins are inherently unstable. Due to stochastic river flow, agreements may be broken in case of drought. The objective of this paper is to analyse whether water allocation agreements can be self-enforcing. An agreement is modelled as the outcome of bargaining game on river water allocation. Given this agreement, the bargaining game is followed by a repeated extensive-form game in which countries decide whether or not to comply with the agreement. I assess under what conditions such agreements are self-enforcing, given stochastic river flow. The results show that, for sufficiently low discounting, every efficient agreement can be sustained in subgame perfect equilibrium. Requiring renegotiation-proofness may shrink the set of possible agreements to a unique self-enforcing agreement. The solution induced by this particular agreement implements the “downstream incremental distribution”, an axiomatic solution to water allocation that assigns all gains from cooperation to downstream countries.Self-Enforcing Agreement, Repeated Extensive-Form Game, Water Allocation, Renegotiation-Proofness

The sequential price of anarchy for atomic congestion games

In situations without central coordination, the price of anarchy relates the quality of any Nash equilibrium to the quality of a global optimum. Instead of assuming that all players choose their actions simultaneously, here we consider games where players choose their actions sequentially. The sequential price of anarchy, recently introduced by Paes Leme, Syrgkanis, and Tardos then relates the quality of any subgame perfect equilibrium to the quality of a global optimum. The effect of sequential decision making on the quality of equilibria, however, depends on the specific game under consideration.\ud Here we analyze the sequential price of anarchy for atomic congestion games with affine cost functions. We derive several lower and upper bounds, showing that sequential decisions mitigate the worst case outcomes known for the classical price of anarchy. Next to tight bounds on the sequential price of anarchy, a methodological contribution of our work is, among other things, a "factor revealing" integer linear programming approach that we use to solve the case of three players

Intra-Household Resource Management Structure and Income-Hiding under Incomplete Information

There is evidence that some multi-person households may withhold income transfers, such as bonuses, gifts, and cash transfers, from other members of the household (Ashraf (2009); Vogler and Pahl, (1994)). In this paper, I show that the incentives to hide income under incomplete information regarding the quantity of resources available to the household differ for three different household resource management structures. I illustrate this with a simple two-stage game. In the first stage, one spouse receives a monetary transfer that is unobserved by her spouse, and she must decide whether to reveal or to hide it. In the second stage, spouses bargain over the allocation of resources between a household good and private expenditure. The three models differ in the resource allocation mechanism that takes place in second stage of the game: housekeeping allowance, independent management, and joint management. Results indicate that when one spouse receives a monetary transfer that is unobservable to her spouse, hiding is more likely to occur in households with a housekeeping allowance contract, compared to independent or joint management. In joint management households, however, a spouse may hide in equilibrium if the change in bargaining power associated with revealing the transfer is not significant enough to compensate for the loss in discretionary expenditure.incomplete information, household bargaining, resource management systems, Demand and Price Analysis, Labor and Human Capital, D13, D82, J12,