An Algorithmic Framework for Strategic Fair Division

We study the paradigmatic fair division problem of allocating a divisible good among agents with heterogeneous preferences, commonly known as cake cutting. Classical cake cutting protocols are susceptible to manipulation. Do their strategic outcomes still guarantee fairness? To address this question we adopt a novel algorithmic approach, by designing a concrete computational framework for fair division---the class of Generalized Cut and Choose (GCC) protocols}---and reasoning about the game-theoretic properties of algorithms that operate in this model. The class of GCC protocols includes the most important discrete cake cutting protocols, and turns out to be compatible with the study of fair division among strategic agents. In particular, GCC protocols are guaranteed to have approximate subgame perfect Nash equilibria, or even exact equilibria if the protocol's tie-breaking rule is flexible. We further observe that the (approximate) equilibria of proportional GCC protocols---which guarantee each of the $n$ agents a $1/n$-fraction of the cake---must be (approximately) proportional. Finally, we design a protocol in this framework with the property that its Nash equilibrium allocations coincide with the set of (contiguous) envy-free allocations

(MU-CTL-01-12) Towards Model Driven Game Engineering in SimSYS: Requirements for the Agile Software Development Process Game

Software Engineering (SE) and Systems Engineering (Sys) are knowledge intensive, specialized, rapidly changing disciplines; their educational infrastructure faces significant challenges including the need to rapidly, widely, and cost effectively introduce new or revised course material; encourage the broad participation of students; address changing student motivations and attitudes; support undergraduate, graduate and lifelong learning; and incorporate the skills needed by industry. Games have a reputation for being fun and engaging; more importantly immersive, requiring deep thinking and complex problem solving. We believe educational games are essential in the next generation of e-learning tools. An extensible, freely available, engaging, problem-based game platform that provides students with an interactive simulated experience closely resembling the activities performed in a (real) industry development project would transform the SE/Sys education infrastructure. Our goal is to extend the state-of-the-art research in SE/Sys education by investigating a game development platform (GDP) from an interdisciplinary perspective (education, game research, and software/systems engineering). A meta-model has been proposed to provide a rigourous foundation that integrates the three disciplines. The GDP is intended to support the semi-automated development of collections of scripted games and their execution, where each game embodies a specific set of learning objectives. The games are scripted using a template based approach. The templates integrate three approaches: use cases; storyboards; and state machines (timed, concurrent, hierarchical state machines). The specification templates capture the structure of the game (Game, Acts, Scenes, Screens, Challenges), storyline, characters (player, non-player, external), graphics, music/sound effects, rules, and so on. The instantiated templates are (manually) transformed into XML game scripts that can be loaded into the SimSYS Game Play Engine. As a game is played, the game play events are logged; they are analyzed to automatically assess a player’s accomplishments and automatically adapt the game play script. Currently, we are manually defining a collection of games. The games are being used to ensure the GDP is flexible and reliable (i.e., the prototype can load and correctly run a variety of game scripts), the ontology is comprehensive, and the templates assist in defining well-organized, modular game scripts. In this report, we present the initial part of an Agile Software Development Process game (Act I, Scenes 1 and 2) that embodies learning objectives related to SE fundamentals (requirements, architecture, testing, process); planning with Gantt charts; working with budgets; and selecting a team for an agile development project. A student player is rewarded in the game by getting hired, scoring points, or getting promoted to lead a project. The game has a variety of settings including a classroom, job fair, and a work environment with meeting rooms, cubicles, and a water cooler station. The main non-player characters include a teacher, boss, and an evil peer. In the future, semi-automated support for creating new game scripts will be explored using a wizard interface. The templates will be formally defined, supporting automated transformation into XML game scripts that can be loaded into the SimSYS Game Engine. We also plan to explore transforming the requirements into a notation that can be imported into a commercial tool that supports Statechart simulation

Strategic Experimentation with Private Payoffs

We consider two players facing identical discrete-time bandit problems with a safe and a risky arm. In any period, the risky arm yields either a success or a failure, and the first success reveals the risky arm to dominate the safe one. When payoffs are public information, the ensuing free-rider problem is so severe that the equilibrium number of experiments is at most one plus the number of experiments that a single agent would perform. When payoffs are private information and players can communicate via cheap talk, the socially optimal symmetric experimentation profile can be supported as a perfect Bayesian equilibrium for sufficiently optimistic prior beliefs. These results generalize to more than two players whenever the success probability per period is not too high. In particular, this is the case when successes occur at the jump times of a Poisson process and the period length is sufficiently small

Resource Buying Games

In resource buying games a set of players jointly buys a subset of a finite resource set E (e.g., machines, edges, or nodes in a digraph). The cost of a resource e depends on the number (or load) of players using e, and has to be paid completely by the players before it becomes available. Each player i needs at least one set of a predefined family S_i in 2^E to be available. Thus, resource buying games can be seen as a variant of congestion games in which the load-dependent costs of the resources can be shared arbitrarily among the players. A strategy of player i in resource buying games is a tuple consisting of one of i's desired configurations S_i together with a payment vector p_i in R^E_+ indicating how much i is willing to contribute towards the purchase of the chosen resources. In this paper, we study the existence and computational complexity of pure Nash equilibria (PNE, for short) of resource buying games. In contrast to classical congestion games for which equilibria are guaranteed to exist, the existence of equilibria in resource buying games strongly depends on the underlying structure of the S_i's and the behavior of the cost functions. We show that for marginally non-increasing cost functions, matroids are exactly the right structure to consider, and that resource buying games with marginally non-decreasing cost functions always admit a PNE

Petri Games: Synthesis of Distributed Systems with Causal Memory

We present a new multiplayer game model for the interaction and the flow of information in a distributed system. The players are tokens on a Petri net. As long as the players move in independent parts of the net, they do not know of each other; when they synchronize at a joint transition, each player gets informed of the causal history of the other player. We show that for Petri games with a single environment player and an arbitrary bounded number of system players, deciding the existence of a safety strategy for the system players is EXPTIME-complete.Comment: In Proceedings GandALF 2014, arXiv:1408.556