Two Influence Maximization Games on Graphs Made Temporal

To address the dynamic nature of real-world networks, we generalize competitive diffusion games and Voronoi games from static to temporal graphs, where edges may appear or disappear over time. This establishes a new direction of studies in the area of graph games, motivated by applications such as influence spreading. As a first step, we investigate the existence of Nash equilibria in competitive diffusion and Voronoi games on different temporal graph classes. Even when restricting our studies to temporal paths and cycles, this turns out to be a challenging undertaking, revealing significant differences between the two games in the temporal setting. Notably, both games are equivalent on static paths and cycles. Our two main technical results are (algorithmic) proofs for the existence of Nash equilibria in temporal competitive diffusion and temporal Voronoi games when the edges are restricted not to disappear over time.

Synthesis of Deceptive Strategies in Reachability Games with Action Misperception

We consider a class of two-player turn-based zero-sum games on graphs with reachability objectives, known as reachability games, where the objective of Player 1 (P1) is to reach a set of goal states, and that of Player 2 (P2) is to prevent this. In particular, we consider the case where the players have asymmetric information about each other's action capabilities: P2 starts with an incomplete information (misperception) about P1's action set, and updates the misperception when P1 uses an action previously unknown to P2. When P1 is made aware of P2's misperception, the key question is whether P1 can control P2's perception so as to deceive P2 into selecting actions to P1's advantage? To answer this question, we introduce a dynamic hypergame model to capture the reachability game with evolving misperception of P2. Then, we present a fixed-point algorithm to compute the deceptive winning region and strategy for P1 under almost-sure winning condition. Finally, we show that the synthesized deceptive winning strategy is at least as powerful as the (non-deceptive) winning strategy in the game in which P1 does not account for P2's misperception. We illustrate our algorithm using a robot motion planning in an adversarial environment.

Swap Stability in Schelling Games on Graphs

We study a recently introduced class of strategic games that is motivated by and generalizes Schelling's well-known residential segregation model. These games are played on undirected graphs, with the set of agents partitioned into multiple types; each agent either occupies a node of the graph and never moves away or aims to maximize the fraction of her neighbors who are of her own type. We consider a variant of this model that we call swap Schelling games, where the number of agents is equal to the number of nodes of the graph, and agents may swap positions with other agents to increase their utility. We study the existence, computational complexity and quality of equilibrium assignments in these games, both from a social welfare perspective and from a diversity perspective.

All-Pay Bidding Games on Graphs

In this paper we introduce and study all-pay bidding games, a class of two player, zero-sum games on graphs. The game proceeds as follows. We place a token on some vertex in the graph and assign budgets to the two players. Each turn, each player submits a sealed legal bid (non-negative and below their remaining budget), which is deducted from their budget and the highest bidder moves the token onto an adjacent vertex. The game ends once a sink is reached, and Player 1 pays Player 2 the outcome that is associated with the sink. The players attempt to maximize their expected outcome. Our games model settings where effort (of no inherent value) needs to be invested in an ongoing and stateful manner. On the negative side, we show that even in simple games on DAGs, optimal strategies may require a distribution over bids with infinite support. A central quantity in bidding games is the ratio of the players budgets. On the positive side, we show a simple FPTAS for DAGs, that, for each budget ratio, outputs an approximation for the optimal strategy for that ratio. We also implement it, show that it performs well, and suggests interesting properties of these games. Then, given an outcome c, we show an algorithm for finding the necessary and sufficient initial ratio for guaranteeing outcome c with probability 1 and a strategy ensuring such. Finally, while the general case has not previously been studied, solving the specific game in which Player 1 wins iff he wins the first two auctions, has been long stated as an open question, which we solve.