Gaming on the edge: using seams in ubicomp games

Outdoor multi-player games are an increasingly popular application area for ubiquitous computing, supporting experimentation both with new technologies and new user experiences. This paper presents an outdoor ubicomp game that exploits the gaps or seams that exist in complex computer systems. Treasure is designed so that players move in and out of areas of wireless network coverage, taking advantage not only of the connectivity within a wireless ‘hotspot’ but of the lack of connectivity outside it. More broadly, this paper discusses how the notion of seamful design can be a source of design ideas for ubicomp games

Connectivity in the presence of an opponent

The paper introduces two player connectivity games played on finite bipartite graphs. Algorithms that solve these connectivity games can be used as subroutines for solving M\"uller games. M\"uller games constitute a well established class of games in model checking and verification. In connectivity games, the objective of one of the players is to visit every node of the game graph infinitely often. The first contribution of this paper is our proof that solving connectivity games can be reduced to the incremental strongly connected component maintenance (ISCCM) problem, an important problem in graph algorithms and data structures. The second contribution is that we non-trivially adapt two known algorithms for the ISCCM problem to provide two efficient algorithms that solve the connectivity games problem. Finally, based on the techniques developed, we recast Horn's polynomial time algorithm that solves explicitly given M\"uller games and provide an alternative proof of its correctness. Our algorithms are more efficient than that of Horn's algorithm. Our solution for connectivity games is used as a subroutine in the algorithm

A concept of weighted connectivity on connected graphs

The introduction of a {0,1}-valued game associated to a connected graph allows us to assign to each node a value of weighted connectivity to the different solutions that for the cooperative games are obtained by means of the semivalues. The marginal contributions of each node to the coalitions differentiate an active connectivity from another reactive connectivity, according to whether the node is essential to obtain the connection or it is the obstacle for the connection between the nodes in the coalition. Diverse properties of this concept of connectivity can be derived.Peer ReviewedPostprint (author’s final draft

Fast winning strategies in Avoider-Enforcer games

In numerous positional games the identity of the winner is easily determined. In this case one of the more interesting questions is not {\em who} wins but rather {\em how fast} can one win. These type of problems were studied earlier for Maker-Breaker games; here we initiate their study for unbiased Avoider-Enforcer games played on the edge set of the complete graph $K_n$ on $n$ vertices. For several games that are known to be an Enforcer's win, we estimate quite precisely the minimum number of moves Enforcer has to play in order to win. We consider the non-planarity game, the connectivity game and the non-bipartite game

Positional games on random graphs

We introduce and study Maker/Breaker-type positional games on random graphs. Our main concern is to determine the threshold probability $p_{F}$ for the existence of Maker's strategy to claim a member of $F$ in the unbiased game played on the edges of random graph $G(n,p)$, for various target families $F$ of winning sets. More generally, for each probability above this threshold we study the smallest bias $b$ such that Maker wins the $(1\:b)$ biased game. We investigate these functions for a number of basic games, like the connectivity game, the perfect matching game, the clique game and the Hamiltonian cycle game

Efficient winning strategies in random-turn Maker-Breaker games

We consider random-turn positional games, introduced by Peres, Schramm, Sheffield and Wilson in 2007. A $p$-random-turn positional game is a two-player game, played the same as an ordinary positional game, except that instead of alternating turns, a coin is being tossed before each turn to decide the identity of the next player to move (the probability of Player I to move is $p$). We analyze the random-turn version of several classical Maker-Breaker games such as the game Box (introduced by Chv\'atal and Erd\H os in 1987), the Hamilton cycle game and the $k$-vertex-connectivity game (both played on the edge set of $K_n$). For each of these games we provide each of the players with a (randomized) efficient strategy which typically ensures his win in the asymptotic order of the minimum value of $p$ for which he typically wins the game, assuming optimal strategies of both players.Comment: 20 page