The assignment game: core bounds for mixed-pair coalitions

In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without changing the coreof the game. These games will be called buyer¿seller exact games and satisfy the condition that each mixed¿pair coalition attains the corresponding matrix entry in the core of the game. For a given assignment game, a unique buyerseller exact assignment game with the same core is proved to exist. In order to identify this matrix and to provide a characterization of those assignment games which are buyer¿seller exact in terms of the assignment matrix, attainable upper and lower core bounds for the mixed¿pair coalitions are found. As a consequence, an open question posed in Quint (1991) regarding a canonical representation of a ¿45o¿lattice¿ by means of the core of an assignment game can now be answered

From caging to rouse dynamics in polymer melts with intramolecular barriers: a critical test of the mode coupling theory

By means of computer simulations and solution of the equations of the mode coupling theory (MCT),we investigate the role of the intramolecular barriers on several dynamic aspects of nonentangled polymers. The investigated dynamic range extends from the caging regime characteristic of glass-formers to the relaxation of the chain Rouse modes. We review our recent work on this question,provide new results, and critically discuss the limitations of the theory. Solutions of the MCT for the structural relaxation reproduce qualitative trends of simulations for weak and moderate barriers. However, a progressive discrepancy is revealed as the limit of stiff chains is approached. This dis-agreement does not seem related with dynamic heterogeneities, which indeed are not enhanced by increasing barrier strength. It is not connected either with the breakdown of the convolution approximation for three-point static correlations, which retains its validity for stiff chains. These findings suggest the need of an improvement of the MCT equations for polymer melts. Concerning the relaxation of the chain degrees of freedom, MCT provides a microscopic basis for time scales from chain reorientation down to the caging regime. It rationalizes, from first principles, the observed deviations from the Rouse model on increasing the barrier strength. These include anomalous scaling of relaxation times, long-time plateaux, and nonmonotonous wavelength dependence of the mode correlators.

A geometric chracterization of the nucleolus of the assignment game

Maschler et al. (1979) caracteritzen geomètricament la intersecció del kernel i del core en els jocs cooperatius, demostrant que les distribucions que pertanyen a ambdós conjunts es troben en el punt mig d’un cert rang de negociació entre parelles de jugadors. En el cas dels jocs d’assignació, aquesta caracterització vol dir que el kernel només conté aquells elements del core on el màxim que un jugador pot transferir a una parella òptima és igual al màxim que aquesta parella li pot transferir, sense sortir-se’n del core. En aquest treball demostrem que el nucleolus d’un joc d’assignació queda caracteritzat si requerim que aquesta propietat de bisecció es compleixi no només per parelles, sinó també per coalicions entre sectors aparellades òptimament.

From caging to rouse dynamics in polymer melts with intramolecular barriers: a critical test of the mode coupling theory

By means of computer simulations and solution of the equations of the mode coupling theory (MCT),we investigate the role of the intramolecular barriers on several dynamic aspects of nonentangled polymers. The investigated dynamic range extends from the caging regime characteristic of glass-formers to the relaxation of the chain Rouse modes. We review our recent work on this question,provide new results, and critically discuss the limitations of the theory. Solutions of the MCT for the structural relaxation reproduce qualitative trends of simulations for weak and moderate barriers. However, a progressive discrepancy is revealed as the limit of stiff chains is approached. This dis-agreement does not seem related with dynamic heterogeneities, which indeed are not enhanced by increasing barrier strength. It is not connected either with the breakdown of the convolution approximation for three-point static correlations, which retains its validity for stiff chains. These findings suggest the need of an improvement of the MCT equations for polymer melts. Concerning the relaxation of the chain degrees of freedom, MCT provides a microscopic basis for time scales from chain reorientation down to the caging regime. It rationalizes, from first principles, the observed deviations from the Rouse model on increasing the barrier strength. These include anomalous scaling of relaxation times, long-time plateaux, and nonmonotonous wavelength dependence of the mode correlators.

A geometric chracterization of the nucleolus of the assignment game

Maschler et al. (1979) caracteritzen geomètricament la intersecció del kernel i del core en els jocs cooperatius, demostrant que les distribucions que pertanyen a ambdós conjunts es troben en el punt mig d’un cert rang de negociació entre parelles de jugadors. En el cas dels jocs d’assignació, aquesta caracterització vol dir que el kernel només conté aquells elements del core on el màxim que un jugador pot transferir a una parella òptima és igual al màxim que aquesta parella li pot transferir, sense sortir-se’n del core. En aquest treball demostrem que el nucleolus d’un joc d’assignació queda caracteritzat si requerim que aquesta propietat de bisecció es compleixi no només per parelles, sinó també per coalicions entre sectors aparellades òptimament.

A cognitive hierarchy model of behavior in the action commitment game

We apply the cognitive hierarchy model of Camerer et al. (Q J Econ 119(3):861-898, 2004)-where players have different levels of reasoning-to Huck et al. (Games Econ Behav 38:240-264, 2002) discrete version of Hamilton and Slutsky (Games Econ Behav 2:29-46, 1990) action commitment game-a duopoly with endogenous timing of entry. We show that, for an empirically reasonable average number of thinking steps, the model rules out Stackelberg equilibria, generates Cournot outcomes including delay, and outcomes where the first mover commits to a quantity higher than Cournot but lower than Stackelberg leader. We show that a cognitive hierarchy model with quantal responses can explain the most important features of the experimental data on the action commitment game in (2002). In order to gauge the success of the model in fitting the data, we compare it to a noisy Nash model. We find that the cognitive hierarchy model with quantal responses fits the data better than the noisy Nash model.

A game-theoretic network formation model

We study the dynamics of a game-theoretic network formation model that yields large-scale small-world networks. So far, mostly stochastic frameworks have been utilized to explain the emergence of these networks. On the other hand, it is natural to seek for game-theoretic network formation models in which links are formed due to strategic behaviors of individuals, rather than based on probabilities. Inspired by Even-Dar and Kearns (2007), we consider a more realistic model in which the cost of establishing each link is dynamically determined during the course of the game. Moreover, players are allowed to put transfer payments on the formation of links. Also, they must pay a maintenance cost to sustain their direct links during the game. We show that there is a small diameter of at most 4 in the general set of equilibrium networks in our model. Unlike earlier model, not only the existence of equilibrium networks is guaranteed in our model, but also these networks coincide with the outcomes of pairwise Nash equilibrium in network formation. Furthermore, we provide a network formation simulation that generates small-world networks. We also analyze the impact of locating players in a hierarchical structure by constructing a strategic model, where a complete b-ary tree is the seed network.

Real options and game theoretical approaches to real estate development projects: multiple equilibria and the implications of different tie-breaking rules

This paper contributes to a fast growing literature which introduces game theory in the analysis of real option investments in a competitive setting. Specifically, in this paper we focus on the issue of multiple equilibria and on the implications that different equilibrium selections may have for the pricing of real options and for subsequent strategic decisions. We present some theoretical results of the necessary conditions to have multiple equilibria and we show under which conditions different tie-breaking rules result in different economic decisions. We then present a numerical exercise using the in formation set obtained on a real estate development in South London. We find that risk aversion reduces option value and this reduction decreases marginally as negative externalities decrease.

The LDC debt problem: a game-theoretical analisys

We review the LDC debt crisis since 1982, by means of game theory. New insights are obtained into the reasons behind the formation of the creditors' carte1 and the nature of the difficu1ties invo1ved in the formation of the debtors' carte1. The standard view that Rubinstein's barganing mode1s are appropriate for dea1ing with debt re1ief is shown to be faulty, un1ess the debtor buys out the debt.

NASH game and mixed H2/H∞ control

In this work a Nonzero-Sum NASH game related to the H2 and H∞ control problems is formulated in the context of convex optimization theory. The variables of the game are limiting bounds for the H2 and H∞ norms, and the final controller is obtained as an equilibrium solution, which minimizes the `sensitivity of each norm' with respect to the other. The state feedback problem is considered and illustrated by numerical examples.

A further note on the college admission game

When a stable matching rule is used for a college admission market, questions on incentives facing agents of both sides of the market naturally emerge. This note states and proves four important results which fill a gap in the theory of incentives for the college admission model. Two of them have never been demonstrated but have been used along the years and are responsible for the success that this theory has had in explaining empirical economic phenomena.

Compensation, Incentives and Risk: Economic Theory and Russian Practise

Mr. Pechersky set out to examine a specific feature of the employer-employee relationship in Russian business organisations. He wanted to study to what extent the so-called "moral hazard" is being solved (if it is being solved at all), whether there is a relationship between pay and performance, and whether there is a correlation between economic theory and Russian reality. Finally, he set out to construct a model of the Russian economy that better reflects the way it actually functions than do certain other well-known models (for example models of incentive compensation, the Shapiro-Stiglitz model etc.). His report was presented to the RSS in the form of a series of manuscripts in English and Russian, and on disc, with many tables and graphs. He begins by pointing out the different examples of randomness that exist in the relationship between employee and employer. Firstly, results are frequently affected by circumstances outside the employee's control that have nothing to do with how intelligently, honestly, and diligently the employee has worked. When rewards are based on results, uncontrollable randomness in the employee's output induces randomness in their incomes. A second source of randomness involves the outside events that are beyond the control of the employee that may affect his or her ability to perform as contracted. A third source of randomness arises when the performance itself (rather than the result) is measured, and the performance evaluation procedures include random or subjective elements. Mr. Pechersky's study shows that in Russia the third source of randomness plays an important role. Moreover, he points out that employer-employee relationships in Russia are sometimes opposite to those in the West. Drawing on game theory, he characterises the Western system as follows. The two players are the principal and the agent, who are usually representative individuals. The principal hires an agent to perform a task, and the agent acquires an information advantage concerning his actions or the outside world at some point in the game, i.e. it is assumed that the employee is better informed. In Russia, on the other hand, incentive contracts are typically negotiated in situations in which the employer has the information advantage concerning outcome. Mr. Pechersky schematises it thus. Compensation (the wage) is W and consists of a base amount, plus a portion that varies with the outcome, x. So W = a + bx, where b is used to measure the intensity of the incentives provided to the employee. This means that one contract will be said to provide stronger incentives than another if it specifies a higher value for b. This is the incentive contract as it operates in the West. The key feature distinguishing the Russian example is that x is observed by the employer but is not observed by the employee. So the employer promises to pay in accordance with an incentive scheme, but since the outcome is not observable by the employee the contract cannot be enforced, and the question arises: is there any incentive for the employer to fulfil his or her promises? Mr. Pechersky considers two simple models of employer-employee relationships displaying the above type of information symmetry. In a static framework the obtained result is somewhat surprising: at the Nash equilibrium the employer pays nothing, even though his objective function contains a quadratic term reflecting negative consequences for the employer if the actual level of compensation deviates from the expectations of the employee. This can lead, for example, to labour turnover, or the expenses resulting from a bad reputation. In a dynamic framework, the conclusion can be formulated as follows: the higher the discount factor, the higher the incentive for the employer to be honest in his/her relationships with the employee. If the discount factor is taken to be a parameter reflecting the degree of (un)certainty (the higher the degree of uncertainty is, the lower is the discount factor), we can conclude that the answer to the formulated question depends on the stability of the political, social and economic situation in a country. Mr. Pechersky believes that the strength of a market system with private property lies not just in its providing the information needed to compute an efficient allocation of resources in an efficient manner. At least equally important is the manner in which it accepts individually self-interested behaviour, but then channels this behaviour in desired directions. People do not have to be cajoled, artificially induced, or forced to do their parts in a well-functioning market system. Instead, they are simply left to pursue their own objectives as they see fit. Under the right circumstances, people are led by Adam Smith's "invisible hand" of impersonal market forces to take the actions needed to achieve an efficient, co-ordinated pattern of choices. The problem is that, as Mr. Pechersky sees it, there is no reason to believe that the circumstances in Russia are right, and the invisible hand is doing its work properly. Political instability, social tension and other circumstances prevent it from doing so. Mr. Pechersky believes that the discount factor plays a crucial role in employer-employee relationships. Such relationships can be considered satisfactory from a normative point of view, only in those cases where the discount factor is sufficiently large. Unfortunately, in modern Russia the evidence points to the typical discount factor being relatively small. This fact can be explained as a manifestation of aversion to risk of economic agents. Mr. Pechersky hopes that when political stabilisation occurs, the discount factors of economic agents will increase, and the agent's behaviour will be explicable in terms of more traditional models.

Optimal game theoretic distributed control methodologies in small scale power systems

This dissertation presents the competitive control methodologies for small-scale power system (SSPS). A SSPS is a collection of sources and loads that shares a common network which can be isolated during terrestrial disturbances. Micro-grids, naval ship electric power systems (NSEPS), aircraft power systems and telecommunication system power systems are typical examples of SSPS. The analysis and development of control systems for small-scale power systems (SSPS) lacks a defined slack bus. In addition, a change of a load or source will influence the real time system parameters of the system. Therefore, the control system should provide the required flexibility, to ensure operation as a single aggregated system. In most of the cases of a SSPS the sources and loads must be equipped with power electronic interfaces which can be modeled as a dynamic controllable quantity. The mathematical formulation of the micro-grid is carried out with the help of game theory, optimal control and fundamental theory of electrical power systems. Then the micro-grid can be viewed as a dynamical multi-objective optimization problem with nonlinear objectives and variables. Basically detailed analysis was done with optimal solutions with regards to start up transient modeling, bus selection modeling and level of communication within the micro-grids. In each approach a detail mathematical model is formed to observe the system response. The differential game theoretic approach was also used for modeling and optimization of startup transients. The startup transient controller was implemented with open loop, PI and feedback control methodologies. Then the hardware implementation was carried out to validate the theoretical results. The proposed game theoretic controller shows higher performances over traditional the PI controller during startup. In addition, the optimal transient surface is necessary while implementing the feedback controller for startup transient. Further, the experimental results are in agreement with the theoretical simulation. The bus selection and team communication was modeled with discrete and continuous game theory models. Although players have multiple choices, this controller is capable of choosing the optimum bus. Next the team communication structures are able to optimize the players’ Nash equilibrium point. All mathematical models are based on the local information of the load or source. As a result, these models are the keys to developing accurate distributed controllers.