Randomness for Free

We consider two-player zero-sum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a) partial-observation (both players have partial view of the game); (b) one-sided complete-observation (one player has complete observation); and (c) complete-observation (both players have complete view of the game). On the basis of mode of interaction we have the following classification: (a) concurrent (both players interact simultaneously); and (b) turn-based (both players interact in turn). The two sources of randomness in these games are randomness in transition function and randomness in strategies. In general, randomized strategies are more powerful than deterministic strategies, and randomness in transitions gives more general classes of games. In this work we present a complete characterization for the classes of games where randomness is not helpful in: (a) the transition function probabilistic transition can be simulated by deterministic transition); and (b) strategies (pure strategies are as powerful as randomized strategies). As consequence of our characterization we obtain new undecidability results for these games

New results on pushdown module checking with imperfect information

Model checking of open pushdown systems (OPD) w.r.t. standard branching temporal logics (pushdown module checking or PMC) has been recently investigated in the literature, both in the context of environments with perfect and imperfect information about the system (in the last case, the environment has only a partial view of the system's control states and stack content). For standard CTL, PMC with imperfect information is known to be undecidable. If the stack content is assumed to be visible, then the problem is decidable and 2EXPTIME-complete (matching the complexity of PMC with perfect information against CTL). The decidability status of PMC with imperfect information against CTL restricted to the case where the depth of the stack content is visible is open. In this paper, we show that with this restriction, PMC with imperfect information against CTL remains undecidable. On the other hand, we individuate an interesting subclass of OPDS with visible stack content depth such that PMC with imperfect information against the existential fragment of CTL is decidable and in 2EXPTIME. Moreover, we show that the program complexity of PMC with imperfect information and visible stack content against CTL is 2EXPTIME-complete (hence, exponentially harder than the program complexity of PMC with perfect information, which is known to be EXPTIME-complete).Comment: In Proceedings GandALF 2011, arXiv:1106.081

A survey of stochastic ω regular games

We summarize classical and recent results about two-player games played on graphs with ω-regular objectives. These games have applications in the verification and synthesis of reactive systems. Important distinctions are whether a graph game is turn-based or concurrent; deterministic or stochastic; zero-sum or not. We cluster known results and open problems according to these classifications

Lynn Magazine - Summer 2008

Main Stories: Degrees of difficulty Composing a masterpiece World of creativityhttps://spiral.lynn.edu/lynnmag/1006/thumbnail.jp

Essays on the use of commitment and tough negotiation tactics in bargaining

This thesis analyses the role of commitment in bargaining. Chapter 1 looks at how players could use finite length commitment to affect the bargaining model in a multiperiod model. The idea of this is to complement the existing literature on infinite length commitment. In line with the infinite commitment literature, a rational player can mimic a commitment type to gain a considerable advantage, although, as will be seen, there are key differences. Chapter 2 analyses whether one should take the opportunity to commit oneself when the opponent does not perfectly observe the decision taken. Logically, if one’s opponent sees no difference between a bluff and actual commitment then one may as well bluff, since the opponent acts the same and committing is a needless sacrifice of freedom. When the opponent may discover a bluff as such, the situation is far less clear and this Chapter analyses when a commitment outcome is likely to prevail. Chapter 3 takes a rather different approach and analyses how hard one should negotiate when there are other parties who may enter the deal. The general finding is that one should follow the crowd and act the same way as everyone else. All three chapters heavily use the mathematical tool of game theory. However, while Chapter 1 uses non-cooperative game theory, the analysis of Chapters 2 and 3 primarily use evolutionary game theory

Semiperfect-information games

Abstract. Much recent research has focused on the applications of games with!-regular objectives in the control and verication of reactive systems. However, many of the game-based models are ill-suited for these applications, because they assume that each player has complete infor-mation about the state of the system (they are \perfect-information" games). This is because in many situations, a controller does not see the private state of the plant. Such scenarios are naturally modeled by \partial-information " games. On the other hand, these games are in-tractable; for example, partial-information games with simple reachabil-ity objectives are 2EXPTIME-complete. We study the intermediate case of \semiperfect-information " games, where one player has complete knowledge of the state, while the other player has only partial knowledge. This model is appropriate in con-trol situations where a controller must cope with plant behavior that is as adversarial as possible, i.e., the controller has partial informa-tion while the plant has perfect information. As is customary, we as-sume that the controller and plant take turns to make moves. We show that these semiperfect-information turn-based games are equiv-alent to perfect-information concurrent games, where the two play-ers choose their moves simultaneously and independently. Since the perfect-information concurrent games are well-understood, we obtain several results of how semiperfect-information turn-based games dif-fer from perfect-information turn-based games on one hand, and from partial-information turn-based games on the other hand. In particular, semiperfect-information turn-based games can benet from randomized strategies while the perfect-information variety cannot, and semiperfect-information turn-based games are in NP \ coNP for all parity objectives.