The Supercore for Normal Form Games

We study the supercore of a system derived from a normal form game. For the case of a finite game with pure strategies, we define a sequence of games and show that the supercore of that system coincides with the set of Nash equilibrium strategy profiles of the last game in the sequence. This result is illustrated with the characterization of the supercore for the n-person prisoners’ dilemma. With regard to the mixed extension of a normal form game, we show that the set of Nash equilibrium profiles coincides with the supercore for games with a finite number of Nash equilibria. For games with an infinite number of Nash equilibria this need not be no longer the case. Yet, it is not difficult to find a binary relation which guarantees the coincidence of these two sets.

Replicator Dynamics and Evolutionary Stable Strategies in Heterogeneous Games

We generalise and extend the work of Iñarra and Laruelle (2011) by studying two person symmetric evolutionary games with two strategies, a heterogenous population with two possible types of individuals and incomplete information. Comparing such games with their classic homogeneous version vith complete information found in the literature, we show that for the class of anti-coordination games the only evolutionarily stable strategy vanishes. Instead, we find infinite neutrally stable strategies. We also model the evolutionary process using two different replicator dynamics setups, each with a different inheritance rule, and we show that both lead to the same results with respect to stability.

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.

Testing the performance and feasibility of Bluetooth communications in pervasive systems

Smart and mobile environments require seamless connections. However, due to the frequent process of ''discovery'' and disconnection of mobile devices while data interchange is happening, wireless connections are often interrupted. To minimize this drawback, a protocol that enables an easy and fast synchronization is crucial. Bearing this in mind, Bluetooth technology appears to be a suitable solution to carry on such connections due to the discovery and pairing capabilities it provides. Nonetheless, the time and energy spent when several devices are being discovered and used at the same time still needs to be managed properly. It is essential that this process of discovery takes as little time and energy as possible. In addition to this, it is believed that the performance of the communications is not constant when the transmission speeds and throughput increase, but this has not been proved formally. Therefore, the purpose of this project is twofold: Firstly, to design and build a framework-system capable of performing controlled Bluetooth device discovery, pairing and communications. Secondly, to analyze and test the scalability and performance of the \emph{classic} Bluetooth standard under different scenarios and with various sensors and devices using the framework developed. To achieve the first goal, a generic Bluetooth platform will be used to control the test conditions and to form a ubiquitous wireless system connected to an Android Smartphone. For the latter goal, various stress-tests will be carried on to measure the consumption rate of battery life as well as the quality of the communications between the devices involved.

Simple Coalitional Strategy Profiles in Repeated Games

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