Invariance under type morphisms: the bayesian Nash equilibrium

Ely and Peski (2006) and Friedenberg and Meier (2010) provide examples when changing the type space behind a game, taking a "bigger" type space, induces changes of Bayesian Nash Equilibria, in other words, the Bayesian Nash Equilibrium is not invariant under type morphisms. In this paper we introduce the notion of strong type morphism. Strong type morphisms are stronger than ordinary and conditional type morphisms (Ely and Peski, 2006), and we show that Bayesian Nash Equilibria are not invariant under strong type morphisms either. We present our results in a very simple, finite setting, and conclude that there is no chance to get reasonable assumptions for Bayesian Nash Equilibria to be invariant under any kind of reasonable type morphisms.

A note on the axiomatization of the Nash equilibrium correspondence

A new axiomatization of the Nash equilibrium correspondence for n-person games based on independence of irrelevant strategies is given. Using a flexible general model, it is proved that the Nash equilibrium correspondence is the only solution to satisfy the axioms of non-emptiness, weak one-person rationality, independence of irrelevant strategies and converse independence of irrelevant strategies on the class of subgames of a fixed finite n-person game which admit at least one Nash equilibrium. It is also shown that these axioms are logically independent.

Game-Theoretically Allocating Resources to Catch Evaders and Payments to Stabilize Teams

Allocating resources optimally is a nontrivial task, especially when multiple

self-interested agents with conflicting goals are involved. This dissertation

uses techniques from game theory to study two classes of such problems:

allocating resources to catch agents that attempt to evade them, and allocating

payments to agents in a team in order to stabilize it. Besides discussing what

allocations are optimal from various game-theoretic perspectives, we also study

how to efficiently compute them, and if no such algorithms are found, what

computational hardness results can be proved.

The first class of problems is inspired by real-world applications such as the

TOEFL iBT test, course final exams, driver's license tests, and airport security

patrols. We call them test games and security games. This dissertation first

studies test games separately, and then proposes a framework of Catcher-Evader

games (CE games) that generalizes both test games and security games. We show

that the optimal test strategy can be efficiently computed for scored test

games, but it is hard to compute for many binary test games. Optimal Stackelberg

strategies are hard to compute for CE games, but we give an empirically

efficient algorithm for computing their Nash equilibria. We also prove that the

Nash equilibria of a CE game are interchangeable.

The second class of problems involves how to split a reward that is collectively

obtained by a team. For example, how should a startup distribute its shares, and

what salary should an enterprise pay to its employees. Several stability-based

solution concepts in cooperative game theory, such as the core, the least core,

and the nucleolus, are well suited to this purpose when the goal is to avoid

coalitions of agents breaking off. We show that some of these solution concepts

can be justified as the most stable payments under noise. Moreover, by adjusting

the noise models (to be arguably more realistic), we obtain new solution

concepts including the partial nucleolus, the multiplicative least core, and the

multiplicative nucleolus. We then study the computational complexity of those

solution concepts under the constraint of superadditivity. Our result is based

on what we call Small-Issues-Large-Team games and it applies to popular

representation schemes such as MC-nets.

As relações de gênero em uma escola de futebol : quando o jogo é possível? = Genders relations at a football school : when the game happen?

Universidade Estadual de Campinas . Faculdade de Educação Física

Multifractal regime transition in a modified minority game model

The search for more realistic modeling of financial time series reveals several stylized facts of real markets. In this work we focus on the multifractal properties found in price and index signals. Although the usual minority game (MG) models do not exhibit multifractality, we study here one of its variants that does. We show that the nonsynchronous MG models in the nonergodic phase is multifractal and in this sense, together with other stylized facts, constitute a better modeling tool. Using the structure function (SF) approach we detected the stationary and the scaling range of the time series generated by the MG model and, from the linear (non-linear) behavior of the SF we identified the fractal (multifractal) regimes. Finally, using the wavelet transform modulus maxima (WTMM) technique we obtained its multifractal spectrum width for different dynamical regimes. (C) 2009 Elsevier Ltd. All rights reserved.

The game inside the school: a representation of 5(th) graders physical education classes

Since the beginning of Physical Education entrance in the brazilin public schools, the game has been frequently used as content, and in the course of time that practice seems to be intensified. In spite of many approaches of different purposes to justify its pedagogic usefulness, the game has been used as an indiscriminate way due to the fascination that it provides to the students. The present study searches for a description and analysis of children`s (10-12 years old) attitudes behaviors in games, on Physical Education classes, inside a public school. The study was accomplished with the researcher also attending as a teacher (action research). For the accomplishment of the study 55 children were filmed in four different games, of different kinds (exposed, transformed, and spontaneous). The classes` description and analysis were focused in the attitude axis and it was defined four topics for the discussion: Conflicts, Respect of rules, Expressiveness, and Competitiveness. The relationship between the individual with the game and its culture were pointed as the main characteristics in the configuration of the ludicrous activity atmosphere. It was also possible to observe specific situations of this relationship, once the games were limited to the social games (Piaget category), in a school atmosphere where children have students roles. Due to the obtained results, the study proposes a reflexive practice in which the students notice their own attitudes and try to adapt the game to their needs and not he other way around. In this perspective, the teacher has an important mediator roll, once he will be responsible to point out the students` difficulties and promote discussions in favor to provide teamwork.

Experimental results on the nonlinear H(infinity) control via quasi-LPV representation and game theory for wheeled mobile robots

In this paper, nonlinear dynamic equations of a wheeled mobile robot are described in the state-space form where the parameters are part of the state (angular velocities of the wheels). This representation, known as quasi-linear parameter varying, is useful for control designs based on nonlinear H(infinity) approaches. Two nonlinear H(infinity) controllers that guarantee induced L(2)-norm, between input (disturbances) and output signals, bounded by an attenuation level gamma, are used to control a wheeled mobile robot. These controllers are solved via linear matrix inequalities and algebraic Riccati equation. Experimental results are presented, with a comparative study among these robust control strategies and the standard computed torque, plus proportional-derivative, controller.

Role of price and enforcement in water allocation: Insights from Game Theory

As many countries are moving toward water sector reforms, practical issues of how water management institutions can better effect allocation, regulation, and enforcement of water rights have emerged. The problem of nonavailability of water to tailenders on an irrigation system in developing countries, due to unlicensed upstream diversions is well documented. The reliability of access or equivalently the uncertainty associated with water availability at their diversion point becomes a parameter that is likely to influence the application by users for water licenses, as well as their willingness to pay for licensed use. The ability of a water agency to reduce this uncertainty through effective water rights enforcement is related to the fiscal ability of the agency to monitor and enforce licensed use. In this paper, this interplay across the users and the agency is explored, considering the hydraulic structure or sequence of water use and parameters that define the users and the agency`s economics. The potential for free rider behavior by the users, as well as their proposals for licensed use are derived conditional on this setting. The analyses presented are developed in the framework of the theory of ""Law and Economics,`` with user interactions modeled as a game theoretic enterprise. The state of Ceara, Brazil, is used loosely as an example setting, with parameter values for the experiments indexed to be approximately those relevant for current decisions. The potential for using the ideas in participatory decision making is discussed. This paper is an initial attempt to develop a conceptual framework for analyzing such situations but with a focus on the reservoir-canal system water rights enforcement.

A vaccination game based on public health actions and personal decisions

Susceptible-infective-removed (SIR) models are commonly used for representing the spread of contagious diseases. A SIR model can be described in terms of a probabilistic cellular automaton (PCA), where each individual (corresponding to a cell of the PCA lattice) is connected to others by a random network favoring local contacts. Here, this framework is employed for investigating the consequences of applying vaccine against the propagation of a contagious infection, by considering vaccination as a game, in the sense of game theory. In this game, the players are the government and the susceptible newborns. In order to maximize their own payoffs, the government attempts to reduce the costs for combating the epidemic, and the newborns may be vaccinated only when infective individuals are found in their neighborhoods and/or the government promotes an immunization program. As a consequence of these strategies supported by cost-benefit analysis and perceived risk, numerical simulations show that the disease is not fully eliminated and the government implements quasi-periodic vaccination campaigns. (C) 2011 Elsevier B.V. All rights reserved.

Strategic argumentation: A game theoretical investigation

Argumentation is modelled as a game where the payoffs are measured in terms of the probability that the claimed conclusion is, or is not, defeasibly provable, given a history of arguments that have actually been exchanged, and given the probability of the factual premises. The probability of a conclusion is calculated using a standard variant of Defeasible Logic, in combination with standard probability calculus. It is a new element of the present approach that the exchange of arguments is analysed with game theoretical tools, yielding a prescriptive and to some extent even predictive account of the actual course of play. A brief comparison with existing argument-based dialogue approaches confirms that such a prescriptive account of the actual argumentation has been almost lacking in the approaches proposed so far.

A note on the multiple partners assignment game

In the assignment game of Shapley and Shubik [Shapley, L.S., Shubik, M., 1972. The assignment game. I. The core, International journal of Game Theory 1, 11-130] agents are allowed to form one partnership at most. That paper proves that, in the context of firms and workers, given two stable payoffs for the firms there is a stable payoff which gives each firm the larger of the two amounts and also one which gives each of them the smaller amount. Analogous result applies to the workers. Sotomayor [Sotomayor, M., 1992. The multiple partners game. In: Majumdar, M. (Ed.), Dynamics and Equilibrium: Essays in Honor to D. Gale. Mcmillian, pp. 322-336] extends this analysis to the case where both types of agents may form more than one partnership and an agent`s payoff is multi-dimensional. Instead, this note concentrates in the total payoff of the agents. It is then proved the rather unexpected result that again the maximum of any pair of stable payoffs for the firms is stable but the minimum need not be, even if we restrict the multiplicity of partnerships to one of the sides. (C) 2009 Elsevier B.V. All rights reserved.

Adjusting prices in the multiple-partners assignment game

Starting with an initial price vector, prices are adjusted in order to eliminate the excess demand and at the same time to keep the transfers to the sellers as low as possible. In each step of the auction, to which set of sellers should those transfers be made is the key issue in the description of the algorithm. We assume additively separable utilities and introduce a novel distinction by considering multiple sellers owing multiple identical objects and multiple buyers with an exogenously defined quota, consuming more than one object but at most one unit of a seller`s good and having multi-dimensional payoffs. This distinction induces a necessarily more complicated construction of the over-demanded sets than the constructions of these sets for the other assignment games. For this approach, our mechanism yields the buyer-optimal competitive equilibrium payoff, which equals the buyer-optimal stable payoff. The symmetry of the model allows to getting the seller-optimal stable payoff and the seller-optimal competitive equilibrium payoff can then be also derived.

The stability of the equilibrium outcomes in the admission games induced by stable matching rules

A stable matching rule is used as the outcome function for the Admission game where colleges behave straightforwardly and the students` strategies are given by their preferences over the colleges. We show that the college-optimal stable matching rule implements the set of stable matchings via the Nash equilibrium (NE) concept. For any other stable matching rule the strategic behavior of the students may lead to outcomes that are not stable under the true preferences. We then introduce uncertainty about the matching selected and prove that the natural solution concept is that of NE in the strong sense. A general result shows that the random stable matching rule, as well as any stable matching rule, implements the set of stable matchings via NE in the strong sense. Precise answers are given to the strategic questions raised.