Bounded Rationality and Repeated Network Formation

We define a finite-horizon repeated network formation game with consent and study the differences induced by two levels of individual rationality. Perfectly rational players will remain unconnected at the equilibrium, while nonempty equilibrium networks may form when players are assumed to behave as finite automata of limited complexity. We provide structural properties of the sequences of networks which are likely to form in Nash and subgame perfect Nash equilibria of the repeated game. For instance, players can form totally different connected networks at each period or the sequence of networks can exhibit a total order relationship.

Three essays on game theory and bargaining

A PhD Dissertation, presented as part of the requirements for the Degree of Doctor of Philosophy from the NOVA - School of Business and Economics

Leniency programs, antitrust enforcement and multimarket contact : three essays in industrial organization

The Layout of My Thesis This thesis contains three chapters in Industrial Organization that build on the work outlined above. The first two chapters combine leniency programs with multimarket contact and provide a thorough analysis of the potential effects of Amnesty Plus and Penalty Plus. The third chapter puts the whole discussion on leniency programs into perspective by examining other enforcement tools available to an antitrust authority. The main argument in that last chapter is that a specific instrument can only be as effective as the policy in which it is embedded. It is therefore important for an antitrust authority to know how it best accompanies the introduction or modification of a policy instrument that helps deterrence. INTRODUCTION Chapter 1 examines the efféct of Amnesty Plus and Penalty Plus on the incentives of firms to report cartel activities. The main question is whether the inclusion of these policies in a leniency program undermine the effectiveness of the latter by discouraging the firms to apply for amnesty. The model is static and focus on the ex post incentives of firms to desist from collusion. The results suggest that, because Amnesty Plus and Penalty Plus encourage the reporting of a second cartel after a first detection, a firm, anticipating this, may be reluctant to seek leniency and to report in the first place. However, the effect may also go in the opposite direction, and Amnesty Plus and Penalty Plus may encourage the simultaneous reporting of two cartels. Chapter 2 takes this idea further to the stage of cartel formation. This chapter provides a complete characterization of the potential anticompetitive and procompetitive effects of Amnesty Plus in a infinitely repeated game framework when the firms use their multimarket contact to harshen punishment. I suggest a clear-cut policy rule that prevents potential adverse effects and thereby show that, if policy makers follow this rule, a leniency program with Amnesty Plus performs better than one without. Chapter 3 characterizes the socially optimal enforcement effort of an antitrust authority and shows how this effort changes with the introduction or modification of specific policy instruments. The intuition is that the policy instrument may increase the marginal benefit of conducting investigations. If this effect is strong enough, a more rigorous detection policy becomes socially desirable.

The Ghost in the Machine: Inferring Machine-Based Strategies from Observed Behavior

We introduce a procedure to infer the repeated-game strategies that generate actions in experimental choice data. We apply the technique to set of experiments where human subjects play a repeated Prisoner's Dilemma. The technique suggests that two types of strategies underly the data.

Dynamics of brand competition: Effects of unobserved social networks

Brand competition is modelled using an agent based approach in order to examine the long run dynamics of market structure and brand characteristics. A repeated game is designed where myopic firms choose strategies based on beliefs about their rivals and consumers. Consumers are heterogeneous and can observe neighbour behaviour through social networks. Although firms do not observe them, the social networks have a significant impact on the emerging market structure. Presence of networks tends to polarize market share and leads to higher volatility in brands. Yet convergence in brand characteristics usually happens whenever the market reaches a steady state. Scale-free networks accentuate the polarization and volatility more than small world or random networks. Unilateral innovations are less frequent under social networks.

A comment on "Rational learning lead to nash equilibrium" by professors Ehud Kalai and Ehud Lehrer

Kalai and Lebrer (93a, b) have recently show that for the case of infinitely repeated games, a coordination assumption on beliefs and optimal strategies ensures convergence to Nash equilibrium. In this paper, we show that for the case of repeated games with long (but finite) horizon, their condition does not imply approximate Nash equilibrium play. Recently Kalai and Lehrer (93a, b) proved that a coordination assumption on beliefs and optimal strategies, ensures that pIayers of an infinitely repeated game eventually pIay 'E-close" to an E-Nash equilibrium. Their coordination assumption requires that if players believes that certain set of outcomes have positive probability then it must be the case that this set of outcomes have, in fact, positive probability. This coordination assumption is called absolute continuity. For the case of finitely repeated games, the absolute continuity assumption is a quite innocuous assumption that just ensures that pIayers' can revise their priors by Bayes' Law. However, for the case of infinitely repeated games, the absolute continuity assumption is a stronger requirement because it also refers to events that can never be observed in finite time.

Foreign support, internal political disputes and mass killings

This paper studies the incentives underlying the relations between foreign countries and rival domestic groups. It models the interaction in a infinitely-repeated game between these three players. The domestic groups bargain for a split of the domestic surplus and may engage in violent dispute for power and in unilateral mass killing processes. The foreign country may choose to support one of these groups in exchange for monetary transfers. The paper characterizes the parametric set in which strategies leading to no violent disputes nor mass killings are Subgame Perfect Nash Equilibra in the presence of foreign support, but not in its absence.

Simple Coalitional Strategy Profiles in Repeated Games

This paper is a version of the discussion paper titled "Simple coalitional strategy profiles"

Endogenous Two-Sided Markets with Repeated Transactions

We consider homogeneous two-sided markets, in which connected buyer-seller pairs bargain and trade repeatedly. In this infinite market game with exogenous matching probabilities and a common discount factor, we prove the existence of equilibria in stationary strategies. The equilibrium payoffs are given implicitly as a solution to a system of linear equations. Then, we endogenize the matching mechanism in a link formation stage that precedes the market game. When agents are sufficiently patient and link costs are low, we provide an algorithm to construct minimally connected networks that are pairwise stable with respect to the expected payoffs in the trading stage. The constructed networks are essentially efficient and consist of components with a constant buyer-seller ratio. The latter ratio increases (decreases) for a buyer (seller) that deletes one of her links in a pairwise stable component.

A Theory of voter experimentation in repeated elections

Nesse artigo, eu desenvolvo e analiso um modelo de dois perí odos em que dois polí ticos competem pela preferência de um eleitor representativo, que sabe quão benevolente é um dos polí ticos mas é imperfeitamente informado sobre quão benevolente é o segundo polí tico. O polí tico conhecido é interpretado como um incumbente de longo prazo, ao passo que o polí tico desconhecido é interpretado como um desa fiante menos conhecido. É estabelecido que o mecanismo de provisão de incentivos inerente às elei cões - que surge através da possibilidade de não reeleger um incumbente - e considerações acerca de aquisi cão de informa cão por parte do eleitor se combinam de modo a determinar que em qualquer equilí brio desse jogo o eleitor escolhe o polí tico desconhecido no per íodo inicial do modelo - uma a cão à qual me refi ro como experimenta cão -, fornecendo assim uma racionaliza cão para a não reelei cão de incumbentes longevos. Especifi camente, eu mostro que a decisão do eleitor quanto a quem eleger no per odo inicial se reduz à compara cão entre os benefí cios informacionais de escolher o polí tico desconhecido e as perdas econômicas de fazê-lo. Os primeiros, que capturam as considera cões relacionadas à aquisi cão de informa cão, são mostrados serem sempre positivos, ao passo que as últimas, que capturam o incentivo à boa performance, são sempre não-negativas, implicando que é sempre ótimo para o eleitor escolher o polí tico desconhecido no per íodo inicial.

Dynamic exercise versus tag game warm up: The acute effect on agility and vertical jump in children

Although dynamic and stretching exercises have been widely investigated, there is little information about warm up performed by tag games. Thus, the purpose of the present study was to verify the acute effect of dynamic exercises compared to a tag game warm up on agility and vertical jump in children. 25 boys and 24 girls participated in this study and performed the agility and vertical jump tests after warm up based on dynamic exercises or as a tag game lasting 10 min each in two different days randomly. Dynamic exercises warm up consisted in a run lasting 2.5 min followed by 2 series of 8 dynamic exercises lasting 10 seconds each interspersed with 20s of light run to recovery. Tag game warm up was performed by a tag game with two variations lasting 5 min each. The first variation there was a single cather, which aimed to get the other participants by touching hands. In the second part of the game, the rules were the same except that the participant that was caught had to help the catcher forming a team of catchers. Warm up intensity was monitored by OMNI perceived exertion scale. ANOVA 2x2 for repeated measures (Warm up x Sex) demonstrated no significant differences between dynamic exercises and tag game for agility and vertical jump (P>0.05) for boys and girls. Perceived exertion was significantly higher in tag game compared to dynamic exercises on girls (P<0.05). Both warm up models showed similar acute effects on agility and vertical jump in children. © Faculty of Education. University of Alicante.

Dynamics of Spatial Game Theory Networks with Novel Modifications

Introduction: Advances in biotechnology have shed light on many biological processes. In biological networks, nodes are used to represent the function of individual entities within a system and have historically been studied in isolation. Network structure adds edges that enable communication between nodes. An emerging fieldis to combine node function and network structure to yield network function. One of the most complex networks known in biology is the neural network within the brain. Modeling neural function will require an understanding of networks, dynamics, andneurophysiology. It is with this work that modeling techniques will be developed to work at this complex intersection. Methods: Spatial game theory was developed by Nowak in the context of modeling evolutionary dynamics, or the way in which species evolve over time. Spatial game theory offers a two dimensional view of analyzingthe state of neighbors and updating based on the surroundings. Our work builds upon this foundation by studying evolutionary game theory networks with respect to neural networks. This novel concept is that neurons may adopt a particular strategy that will allow propagation of information. The strategy may therefore act as the mechanism for gating. Furthermore, the strategy of a neuron, as in a real brain, isimpacted by the strategy of its neighbors. The techniques of spatial game theory already established by Nowak are repeated to explain two basic cases and validate the implementation of code. Two novel modifications are introduced in Chapters 3 and 4 that build on this network and may reflect neural networks. Results: The introduction of two novel modifications, mutation and rewiring, in large parametricstudies resulted in dynamics that had an intermediate amount of nodes firing at any given time. Further, even small mutation rates result in different dynamics more representative of the ideal state hypothesized. Conclusions: In both modificationsto Nowak's model, the results demonstrate the network does not become locked into a particular global state of passing all information or blocking all information. It is hypothesized that normal brain function occurs within this intermediate range and that a number of diseases are the result of moving outside of this range.

Effects of coaches' timeouts on basketball teams' offensive and defensive performances according to momentary differences in score and game period.

The aim of the present study was to assess the effects of game timeouts on basketball teams? offensive and defensive performances according to momentary differences in score and game period. The sample consisted of 144 timeouts registered during 18 basketball games randomly selected from the 2007 European Basketball Championship (Spain). For each timeout, five ball possessions were registered before (n?493) and after the timeout (n?475). The offensive and defensive efficiencies were registered across the first 35 min and last 5 min of games. A k-means cluster analysis classified the timeouts according to momentary score status as follows: losing ( ?10 to ?3 points), balanced ( ?2 to 3 points), and winning (4 to 10 points). Repeated-measures analysis of variance identified statistically significant main effects between pre and post timeout offensive and defensive values. Chi-square analysis of game period identified a higher percentage of timeouts called during the last 5 min of a game compared with the first 35 min (64.999.1% vs. 35.1910.3%; x ?5.4, PB0.05). Results showed higher post timeout offensive and defensive performances. No other effect or interaction was found for defensive performances. Offensive performances were better in the last 5 min of games, with the least differences when in balanced situations and greater differences when in winning situations. Results also showed one interaction between timeouts and momentary differences in score, with increased values when in losing and balanced situations but decreased values when in winning situations. Overall, the results suggest that coaches should examine offensive and defensive performances according to game period and differences in score when considering whether to call a timeout.

Game theory and reciprocity in some extensive form experimental games

We examine decision making in two-person extensive form game trees using nine treatments that vary matching protocol, payoffs, and payoff information. Our objective is to establish replicable principles of cooperative versus noncooperative behavior that involve the use of signaling, reciprocity, and backward induction strategies, depending on the availability of dominated direct punishing strategies and the probability of repeated interaction with the same partner. Contrary to the predictions of game theory, we find substantial support for cooperation under complete information even in various single-play treatments.

A Review on Repeated Games and Reputations with Incomplete Information

In this project we review the effects of reputation within the context of game theory. This is done through a study of two key papers. First, we examine a paper from Fudenberg and Levine: Reputation and Equilibrium Selection in Games with a Patient Player (1989). We add to this a review Gossner’s Simple Bounds on the Value of a Reputation (2011). We look specifically at scenarios in which a long-run player faces a series of short-run opponents, and how the former may develop a reputation. In turn, we show how reputation leads directly to both lower and upper bounds on the long-run player’s payoffs.