Nearly all simulation-based games have environment parameters that affect incentives in the interaction but are not explicitly incorporated into the game model. To understand the impact of these parameters on strategic incentives, typical game-theoretic analysis involves selecting a small set of representative values, and constructing and analyzing separate game models for each value. We introduce a novel technique to learn a single model representing a family of closely related games that differ in the number of symmetric players or other ordinal environment parameters. Prior work trains a multi-headed neural network to output mixed-strategy deviation payoffs, which can be used to compute symmetric $\varepsilon$-Nash equilibria. We extend this work by making environment parameters into input dimensions of the regressor, enabling a single model to learn patterns which generalize across the parameter space. For continuous and discrete parameters, our results show that these generalized models outperform existing approaches, achieving better accuracy with far less data. This technique makes thorough analysis of the parameter space more tractable, and promotes analyses that capture relationships between parameters and incentives.
Congestion games constitute an important class of non-cooperative games which was introduced by Rosenthal in 1973. In recent years, several extensions of these games were proposed to incorporate aspects that are not captured by the standard model. Examples of such extensions include the incorporation of risk sensitive players, the modeling of altruistic player behavior and the imposition of taxes on the resources. These extensions were studied intensively with the goal to obtain a precise understanding of the inefficiency of equilibria of these games. In this paper, we introduce a new model of…
We introduce a way to parameterize automata and games on finite graphs with natural numbers. The parameters are accessed essentially by allowing counting down from the parameter value to 0 and branching depending on whether 0 has been reached. The main technical result is that in games, a player can win for some values of the parameters at all, if she can win for some values below an exponential bound. For many winning conditions, this implies decidability of any statements about a player being able to win with arbitrary quantification over the parameter values. While the result seems broadly …
In the Binary Networked Public Goods game, every player needs to decide if she participates in a public project whose utility is shared equally by the community. We study the problem of deciding if there exists a pure strategy Nash equilibrium (PSNE) in such games. The problem is already known to be NP-complete. We provide fine-grained analysis of this problem under the lens of parameterized complexity theory. We consider various natural graph parameters and show either W[1]-hardness or exhibit an FPT algorithm. We finally exhibit some special graph classes, for example path, cycle, bi-clique,…
Petri games have been introduced as a multi-player game model representing causal memory to address the synthesis of distributed systems. For Petri games with one environment player and an arbitrary bounded number of system players, deciding the existence of a safety strategy is EXPTIME-complete. This result forms the basis of the tool ADAM that implements an algorithm for the synthesis of distributed controllers from Petri games. To evaluate the tool, it has been checked on a series of parameterized benchmarks from manufacturing and workflow scenarios. In this paper, we introduce a new possib…
In recent years, two-player zero-sum games with multiple objectives have received a lot of interest as a model for the synthesis of complex reactive systems. In this framework, Player 1 wins if he can ensure that all objectives are satisfied against any behavior of Player 2. When this is not possible to satisfy all the objectives at once, an alternative is to use some preorder on the objectives according to which subset of objectives Player 1 wants to satisfy. For example, it is often natural to provide more significance to one objective over another, a situation that can be modelled with lexi…
We study a two-player Stackelberg game with incomplete information such that the follower's strategy belongs to a known family of parameterized functions with an unknown parameter vector. We design an adaptive learning approach to simultaneously estimate the unknown parameter and minimize the leader's cost, based on adaptive control techniques and hysteresis switching. Our approach guarantees that the leader's cost predicted using the parameter estimate becomes indistinguishable from its actual cost in finite time, up to a preselected, arbitrarily small error threshold. Also, the first-order n…
