Nash Equilibrium Outcomes Research Articles

Social Protection and Economic Growth

The study deals with the relationship between social protection for workers and economic growth in twenty-five sub-Saharan African (SSA) countries for 2005 and 2006. The regression estimation (using instrumental variables and random effects techniques) includes the logarithm of real GDP, the logarithm of the gross capital formation GCF to GDP (GCF/GDP) ratio, the logarithm of population, the logarithm of the export/GDP ratio, tertiary school enrollment (SET), and social protection rating (SPR). The results show the coefficient of the proxy for capital (GCF/GDP) is insignificant, but the labor variable was shown to have a positive effect on economic growth. Human capital entered the model as tertiary school enrollment (SET). However, the coefficient of SET was not statistically significant, implying that human capital played no part in economic growth in SSA in 2005 and 2006. The SPR variable implies that labor seeks protection and employers resist granting it. Both labor and employers lobby the government and the level of protection achieved is a Nash equilibrium outcome. The income gains to workers if they win cause efficiency losses for society. The SPR variable is positive and statistically significant, indicating that the efficiency losses are less than the income gains by workers. Government promotion of labor, exports, and social protection policies can increase productivity and economic growth.

Implementation in mixed Nash equilibrium

A mechanism implements a social choice correspondence f in mixed Nash equilibrium if, at any preference profile, the set of all (pure and mixed) Nash equilibrium outcomes coincides with the set of f-optimal alternatives for all cardinal representations of the preference profile. Unlike Maskinʼs definition, our definition does not require each optimal alternative to be the outcome of a pure equilibrium. We show that set-monotonicity, a weakening of Maskinʼs monotonicity, is necessary for mixed Nash implementation. With at least three players, set-monotonicity and no-veto power are sufficient. Important correspondences that are not Maskin monotonic can be implemented in mixed Nash equilibrium.

A non-cooperative quality optimization game for scalable video delivery over MANETs

Non-cooperative game theory has found many important applications in engineering. In networking research community, this theory has been adopted to represent the selfish behaviour of the network users. In video transmission over Mobile Ad hoc NETworks (MANETs), video sources try to optimize their perceived video quality unilaterally. On the other hand, network providers try to set some prices on the scarce network resources such that their associated income is maximized. In the current paper, a non-cooperative quality game framework has been introduced in which by exploiting a related quality metric, scalable video users try to optimize their perceived quality in a distributed manner. The existence of a Nash Equilibrium (NE) has been proved and the stability of the distributed resource allocation strategy has been investigated. In the proposed resource assignment game, the utility functions of all competing scalable video sources converge to some optimal value which is dictated by the resulting Nash equilibrium in the allocated rates. In this optimal point, no player (video source) can enhance its utility unilaterally without compromising other players' utility. The assigned rates in the game can be considered as rate-feedbacks for on-line rate adaptation of a moderate scalable video encoder such as H.264/MPEG4 AVC. Some numerical analysis have been presented to validate the theoretical results and to verify the claims.

Network extension

In a model of strategic network formation, the endogenously formed network is built around a pre-existing network. We envisage that the pre-existing or core network is publicly provided. Strategic network formation is decentralized: Players act in their private interest and bear the costs when adding links to the pre-existing network. We study how the pre-existing network affects existence of Nash equilibria and efficiency of Nash equilibrium outcomes: It can foster or prohibit existence of Nash equilibria. It can improve or worsen equilibrium welfare. Special attention is paid to an insider–outsider model where society is partitioned into several groups and links within a group (between insiders) are much cheaper than links across groups (between outsiders). We also present equilibrium existence results and examine the effect of Pareto optimal publicly provided networks.

Optimal Deposit Pricing in Competitive, Oligopolistic Markets

We derive profit-optimal deposit rates in oligopolistic banking markets, considering the depositors' supply sensitivities to deposit rates, the competing banks' deposit rates and non-price factors. The resulting Nash equilibria agree with the empirical literature: Larger banks pay lower deposit rates, the more similar the banks are, the higher are the deposit rates. An increasing market concentration causes a decreasing average deposit rate, bounded from above and below by simple functions of two well-known measures of concentration. Extending our framework to a multi-period economy, relates the common banking approach to value deposits to the microeconomic approach used in industrial organization theory.

Strategic Effects of Renegotiation-Proof Contracts

It is well known that non-renegotiable contracts with third parties may have an effect on the outcome of a strategic interaction and thus serve as a commitment device. We address this issue when contracts are renegotiable. More precisely, we analyze the equilibrium outcomes of two-stage games with renegotiation-proof third-party contracts in relation to the equilibrium outcomes of the same game without contracts. We assume that one of the parties in the contractual relationship is unable to observe everything that happens in the game when played by the other party. We first show that when contracts are non-renegotiable, the set of equilibrium outcomes of the game with contracts is restricted to a subset of Nash equilibrium outcomes of the original game. Introducing renegotiation, in general, imposes further constraints and in some games implies that only subgame perfect equilibrium outcomes of the original game can be supported. However, there is a large class of games in which non-subgame perfect equilibrium outcomes can also be supported, and hence, third-party contracts still have strategic implications even when they are renegotiable.

Evolutionary Determinants of War

This paper considers evolutionarily stable decisions about whether to initiate violent confl‡ict rather than accepting a peaceful sharing outcome. Focusing on small sets of players such as countries in a geographically con fined area, we use Schaffer'’s (1988) concept of evolutionary stability. We find that players' ’evolutionarily stable preferences widen the range of peaceful resource allocations that are rejected in favor of violent con‡flict, compared to the Nash equilibrium outcomes. Relative advantages in fighting strength are re‡flected in the equilibrium set of peaceful resource allocations.

ENDOGENOUS TIMING AND STRATEGIC CHOICE: THE COURNOT‐BERTRAND MODEL

ABSTRACTCournot establishes a Nash equilibrium to a duopoly game under output competition; Bertrand finds a different Nash equilibrium under price competition. Both treat the strategic choice variable (output versus price) and the timing of play as exogenous. We investigate Cournot‐Bertrand models where one firm competes in output and the other competes in price in both static and dynamic settings. We also develop a general model where both the timing of play and the strategic choice variables are endogenous. Consistent with the conduct of Honda and Scion, we show that Cournot‐Bertrand behaviour can be a Nash equilibrium outcome.

Cooperation and evolutionary dynamics in the public goods game with institutional incentives

The one-shot public goods game is extended to include institutional incentives (i.e. reward and/or punishment) that are meant to promote cooperation. It is shown that the Nash equilibrium (NE) outcomes predict either partial or fully cooperative behavior in these extended multi-player games with a continuous strategy space. Furthermore, for some incentive schemes, multiple NE outcomes are shown to emerge. Stability of all these equilibria under standard evolutionary dynamics (i.e. the replicator equation and the canonical equation of adaptive dynamics) is characterized.

Network Games: Theory, Models, and Dynamics

Traditional network optimization focuses on a single control objective in a network populated by obedient users and limited dispersion of information. However, most of today's networks are large-scale with lack of access to centralized information, consist of users with diverse requirements, and are subject to dynamic changes. These factors naturally motivate a new distributed control paradigm, where the network infrastructure is kept simple and the network control functions are delegated to individual agents which make their decisions independently (selfishly). The interaction of multiple independent decision-makers necessitates the use of game theory, including economic notions related to markets and incentives. This monograph studies game theoretic models of resource allocation among selfish agents in networks. The first part of the monograph introduces fundamental game theoretic topics. Emphasis is given to the analysis of dynamics in game theoretic situations, which is crucial for design and control of networked systems. The second part of the monograph applies the game theoretic tools for the analysis of resource allocation in communication networks. We set up a general model of routing in wireline networks, emphasizing the congestion problems caused by delay and packet loss. In particular, we develop a systematic approach to characterizing the inefficiencies of network equilibria, and highlight the effect of autonomous service providers on network performance. We then turn to examining distributed power control in wireless networks. We show that the resulting Nash equilibria can be efficient if the degree of freedom given to end-users is properly designed.

A Note on Endogenous Timing in Duopoly Games

We provide a general analysis of duopoly game in endogenous timing. The Nash equilibrium outcomes are compared with Stackelberg equilibrium outcomes. The different sets of conditions are provided for yielding respectively simultaneous and sequential plays and these conditions only depend on the monotonicities of the reaction functions and the payoffs functions in rival strategic variables.

Evidence of Homo Economicus? Findings from Experiment on Evolutionary Prisoners' Dilemma Game

This paper aims to analyze subjects’ behavior in an experiment on evolutionary process of prisoners’ dilemma game. The experiment has been designed by using sixteen one-shot prisoners’ dilemma games with payoffs perturbation and random matching players under perfect information. The subjects of the experiment were students and staff in Universitas Gadjah Mada, Indonesia. In contrast to previous studies, for instance Selten and Stoecker’s (1986) Cooper’s, et.al (1991, 1996), the majority of the subjects in this experiment tend to choose Nash equilibrium strategy consistently from the first game. The result showed that the proportion of the Nash equilibrium outcome was consistently in the range of 85%-88%, whereas the tacit cooperation or Pareto optimum outcome was about 1%-2%. There were evidence that payoffs perturbation influences players’ decision. In contrast to the previous studies above, the results from this study revealed that the vast majority of the subjects tend to choose the dominant strategy as prescribed in Game Theory.

The Value of Information in Asymmetric All-Pay Auctions

This paper analyzes a two-player all-pay auction with incomplete information. More precisely, one bidder is uncertain about the size of the initial advantage of his rival modeled as a head start in the auction.I derive the unique Bayesian Nash equilibrium outcome for a large class of cumulative distribution functions of the head start.The stronger player generates an informational rent if and only if his head start distribution is not stochastically dominated by a uniform distribution. I identify why my results for an uncertain head start differ qualitatively from uncertainty about a cost function or a valuation.

Efficient Repeated Implementation

This paper examines repeated implementation of a social choice function (SCF) with innitely-lived agents whose preferences are determined randomly in each period. An SCF is repeated-implementable in Nash equilibrium if there exists a sequence of (possibly history-dependent) mechanisms such that (i) its Nash equilibrium set is non-empty and (ii) every Nash equilibrium outcome corresponds to the desired social choice at every possible history of past play and realizations of uncertainty. We show, with minor qualications, that in the complete information environment an SCF is repeated-implementable in Nash equilibrium if and only if it is ecient. We also discuss several extensions of our analysis, including constructions employing only nite mechanisms.

Nationally and Internationally Optimal Climate Policies: External Balances versus Environmental Preferences

This article compares nationally optimal to internationally optimal (Pareto efficient) emission permit levels in a two-country overlapping generations model with national emission permit systems and the environment as a global public good. When each government maximizes its steady state economic and environmental welfare and one country is a net foreign creditor and the other one a net foreign debtor, it is nationally optimal for the creditor country with sufficiently high environmental preferences to chose a stricter permit level than the debtor country. However, the resulting Nash equilibrium permit levels are not Pareto efficient. Depending on the direction and strength of the countries' differences in external balances and environmental preferences, Pareto efficiency mandates that their permit levels are either adjusted in opposite directions or reduced in both. (JEL codes: F59; Q54; D62) Copyright The Author 2010. Published by Oxford University Press on behalf of Ifo Institute for Economic Research, Munich. All rights reserved. For permissions, please email: journals.permissions@oup.com, Oxford University Press.

Technology Adoption in Critical Mass Games: Theory and Experimental Evidence

We analyze the choices between two technologies A and B that both exhibit network eects. We introduce a critical mass game in which coordination on either one of the stan- dards constitutes a Nash equilibrium outcome while coordination on standard B is assumed to be payo¤-dominant. We present a heuristic de…nition of a critical mass and show that the critical mass is inversely related to the mixed strategy equilibrium. We show that the critical mass is closely related to the risk dominance criterion, the global game theory, and the maximin criterion. We present experimental evidence that both the relative degree of payodominance and risk dominance explain players'choices. We …nally show that users' adoption behavior induces …rms to select a relatively unrisky technology which minimizes

Endogenous timing in a mixed oligopoly with semipublic firms

An endogenous order of moves is analyzed in a mixed market where a firm jointly owned by the public sector and private domestic shareholders (a semipublic firm) competes with n private firms. We show that there is an equilibrium in which firms take production decisions simultaneously. This result is strikingly different from that obtained by Pal (Econ Lett 61:181–185, 1998), who shows that when a public firm competes with n private firms all firms producing simultaneously in the same period cannot be sustained as a Subgame Perfect Nash Equilibrium outcome. Our result differs from that of Pal (Econ Lett 61:181–185, 1998) for two reasons: firstly, we consider that there is a semipublic firm rather than a public firm. Secondly, Pal (Econ Lett 61:181–185, 1998) considers that the public firm is less efficient than private firms while in our paper all firms are equally efficient.

When Does Communication Improve Coordination?

We study costless pre-play communication of intentions among inexperienced players. Using the level-k model of strategic thinking to describe players' beliefs, we fully characterize the effects of preplay communication in symmetric 2×2 games. One-way communication weakly increases coordination on Nash equilibrium outcomes, although average payoffs sometimes decrease. Two-way communication further improves payoffs in some games but is detrimental in others. Moving beyond the class of symmetric 2 × 2 games, we find that communication facilitates coordination in common interest games with positive spillovers and strategic complementarities, but there are also games in which any type of communication hampers coordination. (JEL C72, D83)

Strongly Consistent Self-Confirming Equilibrium

Fudenberg and Levine (1993a) introduced the notion of self-confirming equilibrium, which is generally less restrictive than Nash equilibrium. Fudenberg and Levine also defined a concept of consistency, and claimed in their Theorem 4 that with consistency and other conditions on beliefs, a self-confirming equilibrium has a Nash equilibrium outcome. We provide a counterexample that disproves Theorem 4 and prove an alternative by replacing consistency with a more restrictive concept, which we call strong consistency. In games with observed deviators, self-confirming equilibria are strongly consistent self-confirming equilibria. Hence, our alternative theorem ensures that despite the counterexample, the corollary of Theorem 4 is still valid.

Application of Game Theory for Load Balancing in Long Term Evolution Networks

Game theory offers a set of effective tools to be applied in autonomous and distributed self-organizing networks. A typical use case is load balancing which aims at increasing the overall network capacity in case of unequal traffic distribution. The 3GPP Long Term Evolution (LTE) standard provides the means that enables the handover of users from highly loaded cells to the lower loaded neighbors. The method is based on exchanging load information between neighboring cells. However, the computation of the amount of load that a cell should either offload or accept is running autonomously in each cell and ismost likely not generally specified, but rather vendor specific. In this case, a network-wide algorithm for load balancing may not be possible to use if eNodeBs from distinct vendors are deployed. In this game-theoretic analysis for load balancing, we consider each cell as a rational player that decides, in the worst-case, on the amount of load that maximizes its payoff in an uncooperative way. The simulation results for LTE network show that the resulting Nash equilibrium is able to achieve most of the gain expected from a strictly cooperative load balancing scheme. Though each cell acts independently, the Nash equilibrium almost provides the sameperformanceof a network-wide algorithm for load balancingwhichwould ease the players to decide on strategies that aremore collaborative. The capacity gain of theNash equilibrium is verified for the homogeneous network layout, different scenarios and parameter configurations. Moreover, to take real network effects, such as different cell sizes and number of neighbor cells into consideration, the Nash equilibrium is also tested in the heterogeneous network layout. Index Terms – Game theory, Load balancing, Self optimizing network, Distributed systems.