We study the alternating-time temporal logic ATL+ enriched with one resource (written ATL+(1)) extending ATL+ with the possibility to manage a budget. We propose a game-theoretic semantics via the introduction of two evaluation games so that the compositional semantics is captured by strategies in the games. We show that the model-checking problem for ATL+(1) is in PSpace and we identify several non-trivial fragments that can be solved in PTime. By-products of our investigations include also a simplified Pspace decision procedure for resource-free ATL+, an effective way to synthesize constraints in a version of ATL+(1) with parameters and a PSpace bound to solve an energy game with one counter whose objectives are LTL formulae of temporal depth one.

This paper investigates repeated win-lose coordination games (WLC-games). We analyze which protocols are optimal for these games, covering both the worst case and average case scenarios, i,e., optimizing the guaranteed and expected coordination times. We begin by analyzing Choice Matching Games (CM-games) which are a simple yet fundamental type of WLC-games, where the goal of the players is to pick the same choice from a finite set of initially indistinguishable choices. We give a fully complete classification of optimal expected and guaranteed coordination times in two-player CM-games and show that the corresponding optimal protocols are unique in every case—except in the CM-game with four choices, which we analyze separately. Our results on CM-games are essential for proving a more general result on the difficulty of all WLC-games: we provide a complete analysis of least upper bounds for optimal expected coordination times in all two-player WLC-games as a function of game size. We also show that CM-games can be seen as the most difficult games among all two-player WLC-games, as they turn out to have the greatest optimal expected coordination times.

We study the expressive power of logics whose truth is defined over sets of assignments, called teams, instead of single assignments. Given a team X, any k-tuple of variables in the domain of X defines a corresponding k-ary team relation. Thus the expressive power of a logic L with team semantics amounts to the set of properties of team relations which L-formulas can define. We introduce a concept of k-invariance which is a natural semantic restriction on any atomic formulae with team semantics. Then we develop a novel proof method to show that, if L is an extension of FO with any k-invariant atoms, then there are such properties of (k+1)-ary team relations which cannot be defined in L. This method can be applied e.g. for arity fragments of various logics with team semantics to prove undefinability results. In particular, we make some interesting observations on the definability of binary team relations with unary inclusion-exclusion logic.

We investigate repeated win-lose coordination games and analyse when and how rational players can guarantee eventual coordination in such games. Our study involves both the setting with a protocol shared in advance as well as the scenario without an agreed protocol. In both cases, we focus on the case without any communication amongst the players once the particular game to be played has been revealed to them. We identify classes of coordination games in which coordination cannot be guaranteed in a single round, but can eventually be achieved in several rounds by following suitable coordination protocols. In particular, we study coordination using protocols invariant under structural symmetries of games under some natural assumptions, such as: Priority hierarchies amongst players, different patience thresholds, use of focal groups, and gradual coordination by contact.

Abstract We study pure coordination games where in every outcome, all players have identical payoffs, ‘win’ or ‘lose’. We identify and discuss a range of ‘purely rational principles’ guiding the reasoning of rational players in such games and compare the classes of coordination games that can be solved by such players with no preplay communication or conventions. We observe that it is highly nontrivial to delineate a boundary between purely rational principles and other decision methods, such as conventions, for solving such coordination games.

We introduce several versions of game-theoretic semantics (GTS) for Alternating-Time Temporal Logic (ATL). In GTS, truth is defined in terms of existence of a winning strategy in a semantic evaluation game. Thus, the game-theoretic perspective appears in the framework of ATL on two semantic levels: on the object level in the standard semantics of the strategic operators and on the meta-level, where game-theoretic logical semantics is applied to ATL. We unify these two perspectives into semantic evaluation games specially designed for ATL. The game-theoretic perspective enables us to identify new variants of the semantics of ATL based on limiting the time resources available to the verifier and falsifier in the semantic evaluation game. We introduce and analyze an unbounded and (ordinal) bounded GTS and prove these to be equivalent to the standard (Tarski-style) compositional semantics. We show that, in bounded GTS, truth of ATL formulae can always be determined in finite time, that is, without constructing infinite paths. We also introduce a nonequivalent finitely bounded semantics and argue that it is natural from both logical and game-theoretic perspectives.

We consider a variation of the branching time logic CTL with non-standard, "finitely bounded" semantics (FBS). FBS is naturally defined as game-theoretic semantics where the proponent of truth of an eventuality must commit to a time limit (number of transition steps) within which the formula should become true on all (resp. some) paths starting from the state where the formula is evaluated. The resulting version CTL(FB) of CTL differs essentially from the standard one as it no longer has the finite model property. We develop two tableaux systems for CTL(FB). The first one deals with infinite sets of formulae, whereas the second one deals with finite sets of formulae in a slightly extended language allowing explicit indication of time limits in formulae. We prove soundness and completeness of both systems and also show that the latter tableaux system provides an EXPTIME decision procedure for it and thus prove EXPTIME-completeness of the satisfiability problem.