Games with perceptions

We assume that 2 x 2 matrix games are publicly known and that players perceive a dichotomous characteristic on their opponents which defines two types for each player. In turn, each type has beliefs concerning her opponent's types, and payoffs are assumed to be type-independent. We analyze whether the mere possibility of different types playing different strategies generates discriminatory equilibria. Given a specific information structure we find that in equilibrium a player discriminates between her types if and only if her opponent does so. We also find that for dominant solvable 2x2 games no discriminatory equilibrium exists, while under different conditions of concordance between players' beliefs discrimination appears for coordination and for competitive games. A complete characterization of the set of Bayesian equilibria is provided.

The von Neumann-Morgenstern stable sets for 2x2 games

We analyze the von Neumann and Morgenstern stable sets for the mixed extension of 2 2 games when only single profitable deviations are allowed. We show that the games without a strict Nash equilibrium have a unique vN&M stable set and otherwise they have infinite sets.

Learning in Network Games

We report the findings of an experiment designed to study how people learn and make decisions in network games. Network games offer new opportunities to identify learning rules, since on networks (compared to e.g. random matching) more rules differ in terms of their information requirements. Our experimental design enables us to observe both which actions participants choose and which information they consult before making their choices. We use this information to estimate learning types using maximum likelihood methods. There is substantial heterogeneity in learning types. However, the vast majority of our participants' decisions are best characterized by reinforcement learning or (myopic) best-response learning. The distribution of learning types seems fairly stable across contexts. Neither network topology nor the position of a player in the network seem to substantially affect the estimated distribution of learning types.

A monotonic core concept for convex games: The SD-prenucleolus

We prove that the SD-prenucleolus satisfies monotonicity in the class of convex games. The SD-prenucleolus is thus the only known continuous core concept that satisfies monotonicity for convex games. We also prove that for convex games the SD-prenucleolus and the SD-prekernel coincide.

Playing games with words cultural transfer in David Lynch's Blue Velvet

Eguíluz, Federico; Merino, Raquel; Olsen, Vickie; Pajares, Eterio; Santamaría, José Miguel (eds.)

Tameside College: Triptico games and resources used to engage students

Tracey Holt introduced Triptico to her department after attending training from Sue Shercliff, ESOL Lecturer. Triptico is a resource for teachers to use in conjunction with their interactive whiteboards that currently contains around 20 different interactive resources - all of which can be easily edited, adapted and saved for later use. This quickly spread throughout the entire college. It is a fantastic free resource which promotes more interaction in the classroom between the teacher and students.

Lancaster and Morecambe College: Uses serious computer games as a teaching tool

John Latham, International Projects Co-ordinator at Lancaster and Morecambe College (LMC), got involved with the project Serious Computer Games as a Teaching Tool (SCOGATT) after using the game EnerCities with his students. The web based platform at www.scogatt.eu serves as a One Stop Toolkit for vocational teachers and trainers who want to use serious computer games (SCG) in their teaching environments but might need a helping hand. There they will be able to find a compendium of serious games, SCOGATT pilot results, teacher reports and the exemplar games, EnerCities.

Coalitional games with veto players: Myopic and farsighted behavior

This paper studies an allocation procedure for coalitional games with veto players. The procedure is similar to the one presented by Dagan et al. (1997) for bankruptcy problems. According to it, a player, the proposer, makes a proposal that the remaining players must accept or reject, and con ict is solved bilaterally between the rejector and the proposer. We allow the proposer to make sequential proposals over several periods. If responders are myopic maximizers (i.e. consider each period in isolation), the only equilibrium outcome is the serial rule of Arin and Feltkamp (2012) regardless of the order of moves. If all players are farsighted, the serial rule still arises as the unique subgame perfect equilibrium outcome if the order of moves is such that stronger players respond to the proposal after weaker ones.

On the impact of independence of irrelevant alternatives: the case of two-person NTU games

On several classes of n-person NTU games that have at least one Shapley NTU value, Aumann characterized this solution by six axioms: Non-emptiness, efficiency, unanimity, scale covariance, conditional additivity, and independence of irrelevant alternatives (IIA). Each of the first five axioms is logically independent of the remaining axioms, and the logical independence of IIA is an open problem. We show that for n = 2 the first five axioms already characterize the Shapley NTU value, provided that the class of games is not further restricted. Moreover, we present an example of a solution that satisfies the first five axioms and violates IIA for two-person NTU games (N, V) with uniformly p-smooth V(N).

The Relevance of Relative Position in Ultimatum Games

This paper investigates the effect of focal points and initial relative position in the outcome of a bargaining process. We conduct two on-line experiments. In the first experiment we attempt to replicate Güth, Huck and Müller's (2001) results about the relevance of equal splits. In our second experiment, we recover the choices of participants in forty mini-ultimatum games. This design allows us to test whether the equal split or any other distribution or set of distributions are salient. Our data provide no support for a focal-point explanation but we find support for an explanation based on relative position. Our results confirm that there is a norm against hyper-fair offers. Proposers are expected to behave selfishly when the unselfish distribution leads to a change in the initial relative position.

Simple Coalitional Strategy Profiles in Repeated Games

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

Characterizing distribution rules for cost sharing games

In noncooperative cost sharing games, individually strategic agents choose resources based on how the welfare (cost or revenue) generated at each resource (which depends on the set of agents that choose the resource) is distributed. The focus is on finding distribution rules that lead to stable allocations, which is formalized by the concept of Nash equilibrium, e.g., Shapley value (budget-balanced) and marginal contribution (not budget-balanced) rules.

Recent work that seeks to characterize the space of all such rules shows that the only budget-balanced distribution rules that guarantee equilibrium existence in all welfare sharing games are generalized weighted Shapley values (GWSVs), by exhibiting a specific 'worst-case' welfare function which requires that GWSV rules be used. Our work provides an exact characterization of the space of distribution rules (not necessarily budget-balanced) for any specific local welfare functions remains, for a general class of scalable and separable games with well-known applications, e.g., facility location, routing, network formation, and coverage games.

We show that all games conditioned on any fixed local welfare functions possess an equilibrium if and only if the distribution rules are equivalent to GWSV rules on some 'ground' welfare functions. Therefore, it is neither the existence of some worst-case welfare function, nor the restriction of budget-balance, which limits the design to GWSVs. Also, in order to guarantee equilibrium existence, it is necessary to work within the class of potential games, since GWSVs result in (weighted) potential games.

We also provide an alternative characterization—all games conditioned on any fixed local welfare functions possess an equilibrium if and only if the distribution rules are equivalent to generalized weighted marginal contribution (GWMC) rules on some 'ground' welfare functions. This result is due to a deeper fundamental connection between Shapley values and marginal contributions that our proofs expose—they are equivalent given a transformation connecting their ground welfare functions. (This connection leads to novel closed-form expressions for the GWSV potential function.) Since GWMCs are more tractable than GWSVs, a designer can tradeoff budget-balance with computational tractability in deciding which rule to implement.

Voting games with incomplete information

We examine voting situations in which individuals have incomplete information over each others' true preferences. In many respects, this work is motivated by a desire to provide a more complete understanding of so-called probabilistic voting.

Chapter 2 examines the similarities and differences between the incentives faced by politicians who seek to maximize expected vote share, expected plurality, or probability of victory in single member: single vote, simple plurality electoral systems. We find that, in general, the candidates' optimal policies in such an electoral system vary greatly depending on their objective function. We provide several examples, as well as a genericity result which states that almost all such electoral systems (with respect to the distributions of voter behavior) will exhibit different incentives for candidates who seek to maximize expected vote share and those who seek to maximize probability of victory.

In Chapter 3, we adopt a random utility maximizing framework in which individuals' preferences are subject to action-specific exogenous shocks. We show that Nash equilibria exist in voting games possessing such an information structure and in which voters and candidates are each aware that every voter's preferences are subject to such shocks. A special case of our framework is that in which voters are playing a Quantal Response Equilibrium (McKelvey and Palfrey (1995), (1998)). We then examine candidate competition in such games and show that, for sufficiently large electorates, regardless of the dimensionality of the policy space or the number of candidates, there exists a strict equilibrium at the social welfare optimum (i.e., the point which maximizes the sum of voters' utility functions). In two candidate contests we find that this equilibrium is unique.

Finally, in Chapter 4, we attempt the first steps towards a theory of equilibrium in games possessing both continuous action spaces and action-specific preference shocks. Our notion of equilibrium, Variational Response Equilibrium, is shown to exist in all games with continuous payoff functions. We discuss the similarities and differences between this notion of equilibrium and the notion of Quantal Response Equilibrium and offer possible extensions of our framework.

Los “serious games” como herramienta docente para el fomento del emprendimiento:concurso e-mprende UPV/EHU

La sociedad está sometida a un proceso de cambio constante y las metodologías docentes deben adaptarse también a estos cambios. Hemos decidido realizar el presente Trabajo de Fin de Grado con el fin de poner en valor la utilidad de las metodologías docentes más innovadoras que consigan adaptar la docencia a la sociedad moderna. Así pues, explicamos lo que son los Serious Games y los usos que pueden tener en la docencia desde el punto de vista del emprendimiento empresarial. Como ejemplo más cercano de Serious Game, utilizamos el simulador del concurso E-mprende, un concurso diseñado para estudiantes que enfrenta a los usuarios a través de un Simulador empresarial. Se trata de un Business Game desarrollado entre otros por la Universidad del País Vasco que intenta enseñar a los jugadores lo que es dirigir una empresa de nueva creación dándoles el control virtual de la misma a través de una plataforma web donde deberán tomar una serie de rondas de decisiones. Para comenzar, realizamos un análisis bibliográfico con el fin de dar una correcta explicación de lo que son los juegos, los Serious Games y los Business Games. Básicamente, un Serious Game se diferencia de un Juego ordinario en su finalidad. Mientras que un juego ordinario se ha diseñado con el único fin de divertir, el Juego Serio también tiene el objetivo de formar, entrenar o educar. Por su parte, Un Business Game es un Serious Game diseñado para el ámbito de los negocios en el que se pretende formar al jugador en materia de empresas. Realizando ese análisis bibliográfico, obtenemos una serie de conclusiones que podremos contrastar utilizando como ejemplo el simulador del concurso emprende. Para conseguir datos totalmente verídicos, elaboramos un cuestionario a medida destinado a los participantes del concurso que se entregó al finalizar el concurso. Dado que este Trabajo de Fin de Grado se enmarca en el ámbito del emprendimiento, lo que nos interesa contrastar por encima de todo es si el hecho de participar en un Business Game como el del concurso E-mprende ayuda a fomentar el espíritu emprendedor en el alumno más allá de complementar conocimientos teóricos y prácticos, lo cual no deja de ser importante.