The Curse of Ties in Congestion Games with Limited Lookahead

Abstract: We introduce a novel framework to model limited lookahead in congestion games. Intuitively, the players enter the game sequentially and choose an optimal action under the assumption that the $k-1$ subsequent players play subgame-perfectly. Our model naturally interpolates between outcomes of greedy best-response ($k=1$) and subgame-perfect outcomes ($k=n$, the number of players). We study the impact of limited lookahead (parameterized by $k$) on the stability and inefficiency of the resulting outcomes. As our results reveal, increased lookahead does not necessarily lead to better outcomes; in fact, its effect crucially depends on the existence of ties and the type of game under consideration. More specifically, already for very simple network congestion games we show that subgame-perfect outcomes (full lookahead) can be unstable, whereas greedy best-response outcomes (no lookahead) are known to be stable. We show that this instability is due to player indifferences (ties). If the game is generic (no ties exist) then all outcomes are stable, independent of the lookahead $k$. In particular, this implies that the price of anarchy of $k$-lookahead outcomes (for arbitrary $k$) equals the standard price of anarchy. For special cases of cost-sharing games and consensus games we show that no lookahead leads to stable outcomes. Again this can be resolved by removing ties, though for cost-sharing games only full lookahead provides stable outcomes. We also identify a class of generic cost-sharing games for which the inefficiency decreases as the lookahead $k$ increases.