Cannibal Animal Games: A new variant of Tic-Tac-Toe

This paper presents a new partial two-player game, called the cannibal animal game, which is a variant of Tic-Tac-Toe. The game is played on the infinite grid, where in each round a player chooses and occupies free cells. The first player Alice can occupy a cell in each turn and wins if she occupies a set of cells, the union of a subset of which is a translated, reflected and/or rotated copy of a previously agreed upon polyomino P (called an animal). The objective of the second player Bob is to prevent Alice from creating her animal by occupying in each round a translated, reflected and/or rotated copy of P. An animal is a cannibal if Bob has a winning strategy, and a non-cannibal otherwise. This paper presents some new tools, such as the bounding strategy and the punching lemma, to classify animals into cannibals or non-cannibals. We also show that the pairing strategy works for this problem.

Characterizing multi-agent team behavior from partial team tracings : evidence from the English Premier League

Real-world AI systems have been recently deployed which can automatically analyze the plan and tactics of tennis players. As the game-state is updated regularly at short intervals (i.e. point-level), a library of successful and unsuccessful plans of a player can be learnt over time. Given the relative strengths and weaknesses of a player’s plans, a set of proven plans or tactics from the library that characterize a player can be identified. For low-scoring, continuous team sports like soccer, such analysis for multi-agent teams does not exist as the game is not segmented into “discretized” plays (i.e. plans), making it difficult to obtain a library that characterizes a team’s behavior. Additionally, as player tracking data is costly and difficult to obtain, we only have partial team tracings in the form of ball actions which makes this problem even more difficult. In this paper, we propose a method to overcome these issues by representing team behavior via play-segments, which are spatio-temporal descriptions of ball movement over fixed windows of time. Using these representations we can characterize team behavior from entropy maps, which give a measure of predictability of team behaviors across the field. We show the efficacy and applicability of our method on the 2010-2011 English Premier League soccer data.

Zero-Sum Stochastic Games with Partial Information and Average Payoff

We consider a discrete time partially observable zero-sum stochastic game with average payoff criterion. We study the game using an equivalent completely observable game. We show that the game has a value and also we present a pair of optimal strategies for both the players.

Strategic behavior under partial cooperation

We investigate how a group of players might cooperate with each other within the setting of a non-cooperative game. We pursue two notions of partial cooperative equilibria that follow a modification of Nash's best response rationality rather than a core-like approach. Partial cooperative Nash equilibrium treats non-cooperative players and the coalition of cooperators symmetrically, while the notion of partial cooperative leadership equilibrium assumes that the group of cooperators has a first-mover advantage. We prove existence theorems for both types of equilibria. We look at three well-known applications under partial cooperation. In a game of voluntary provision of a public good we show that our two new equilibrium notions of partial cooperation coincide. In a modified Cournot oligopoly, we identify multiple equilibria of each type and show that a non-cooperator may have a higher payoff than a cooperator. In contrast, under partial cooperation in a symmetric Salop City game, a cooperator enjoys a higher return.

Web Services and Incerta Spiriti: A Game Theoretic Approach to Uncertainty

A web-service is a remote computational facility which is made available for general use by means of the internet. An orchestration is a multi-threaded computation which invokes remote services. In this paper game theory is used to analyse the behaviour of orchestration evaluations when underlying web-services are unreliable. Uncertainty profiles are proposed as a means of defining bounds on the number of service failures that can be expected during an orchestration evaluation. An uncertainty profile describes a strategic situation that can be analyzed using a zero-sum angel-daemon game with two competing players: an angel a whose objective is to minimize damage to an orchestration and a daemon d who acts in a destructive fashion. An uncertainty profile is assessed using the value of its angel daemon game. It is shown that uncertainty profiles form a partial order which is monotonic with respect to assessment.

Game-­theoretic Resource Allocation with Real-­time Probabilistic Surveillance Information

Game-theoretic security resource allocation problems have generated significant interest in the area of designing and developing security systems. These approaches traditionally utilize the Stackelberg game model for security resource scheduling in order to improve the protection of critical assets. The basic assumption in Stackelberg games is that a defender will act first, then an attacker will choose their best response after observing the defender’s strategy commitment (e.g., protecting a specific asset). Thus, it requires an attacker’s full or partial observation of a defender’s strategy. This assumption is unrealistic in real-time threat recognition and prevention. In this paper, we propose a new solution concept (i.e., a method to predict how a game will be played) for deriving the defender’s optimal strategy based on the principle of acceptable costs of minimax regret. Moreover, we demonstrate the advantages of this solution concept by analyzing its properties.

Partial Cooperation in Strategic Decision Situations

We consider a normal form game in which there is a single exogenously given coalition of cooperating players that can write a binding agreement on pre-selected actions. These collective actions typically represent a certain number of dimensions in the players’ strategy space. The actions represented by the other dimensions of the strategy space remain under the complete, individual control of the players.
We consider a standard extension of the Nash equilibrium concept denoted as a partial cooperative equilibrium as well as an equilibrium concept in which the coalition of cooperators has a leadership position. Existence results are developed for these new equilibrium concepts. We identify conditions on these partial cooperative games under which the various equilibrium concepts are equivalent.
We apply this game theoretic framework to existing models of multi-market oligopolies and international pollution abatement. In a multi-market oligopoly typically a merger paradox emerges in the partial cooperative equilibrium, which vanishes if the cartel of collaborators exploits its leadership position. Our application to international pollution abatement treaties shows that cooperation by a sufficiently large group of countries results in a Pareto improvement over the standard tragedy of the commons outcome described by the Nash equilibrium.

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.

Partial Cooperation in Location Choice: Salop’s Model with Three Firms

We consider how three firms compete in a Salop location model and how cooperation in location choice by two of these firms affects the outcomes. We con- sider the classical case of linear transportation costs as a two-stage game in which the firms select first a location on a unit circle along which consumers are dispersed evenly, followed by the competitive selection of a price. Standard analysis restricts itself to purely competitive selection of location; instead, we focus on the situation in which two firms collectively decide about location, but price their products competitively after the location choice has been effectuated. We show that such partial coordination of location is beneficial to all firms, since it reduces the number of equilibria significantly and, thereby, the resulting coordination problem. Subsequently, we show that the case of quadratic transportation costs changes the main conclusions only marginally.

Phylogeographic Triangulation: Using Predator-Prey-Parasite Interactions to Infer Population History from Partial Genetic Information

Phylogeographic studies, which infer population history and dispersal movements from intra-specific spatial genetic variation, require expensive and time-consuming analyses that are not always feasible, especially in the case of rare or endangered species. On the other hand, comparative phylogeography of species involved in close biotic interactions may show congruent patterns depending on the specificity of the relationship. Consequently, the phylogeography of a parasite that needs two hosts to complete its life cycle should reflect population history traits of both hosts. Population movements evidenced by the parasite’s phylogeography that are not reflected in the phylogeography of one of these hosts may thus be attributed to the other host. Using the wild rabbit (Oryctolagus cuniculus) and a parasitic tapeworm (Taenia pisiformis) as an example, we propose comparing the phylogeography of easily available organisms such as game species and their specific heteroxenous parasites to infer population movements of definitive host/predator species, independently of performing genetic analyses on the latter. This may be an interesting approach for indirectly studying the history of species whose phylogeography is difficult to analyse directly.

Meaning in movement : a gestural design game

This paper describes a design game that we called 'Meaning in Movement'. The purpose was to explore notions of professional dental practice with dental practioners in terms of gestures, actions and movements. The game represents a first step towards involving gestures, actions and movements in a design dialog with practioners for the purpose of designing future interactive systems which are more appropriate to the type of skilful actions and richly structured environments of dentists and dental assistants.