The curse of simultaneity

Abstract

Typical models of strategic interactions in computer science use simultaneous move games. However, in applications simultaneity is often hard or impossible to achieve. In this paper, we study the robustness of the Nash Equilibrium when the assumption of simultaneity is dropped. In particular we propose studying the sequential price of anarchy: the quality of outcomes of sequential versions of games whose simultaneous counterparts are prototypical in algorithmic game theory. We study different classes of games with high price of anarchy, and show that the subgame perfect equilibrium of their sequential version is a much more natural prediction, ruling out unreasonable equilibria, and leading to much better quality solutions.We consider three examples of such games: Cost Sharing Games, Unrelated Machine Scheduling Games and Consensus Games. For Machine Cost Sharing Games, the sequential price of anarchy is at most O(log(n)), an exponential improvement of the O(n) price of anarchy of their simultaneous counterparts. Further, the subgame perfect equilibrium can be computed by a polynomial time greedy algorithm, and is independent of the order the players arrive. For Unrelated Machine Scheduling Games we show that the sequential price of anarchy is bounded as a function of the number of jobs n and machines m (by at most O(m2 n )), while in the simultaneous version the price of anarchy is unbounded even for two players and two machines. For Consensus Games we observe that the optimal outcome for generic weights is the unique equilibrium that arises in the sequential game. We also study the related Cut Games, where we show that the *

Non-Cooperative Facility Location Games: a Survey

“…These instances explore the fact that players move simultaneously when represented in normal form. When sequentiality [25] is considered, Rodrigues and Xavier [19] prove that the PoA for Metric Capacitated FLG has a bound of Θ(2 k ).…”

“…For facility location games, and specially for the capacitated version, it is useful to consider what changes when these games are sequential [25]. To analyze these scenarios, the concept of Subgame Perfect Equilibrium (SPE) is used instead of PNE.…”

“…Nonetheless, few have been explored in the context of facility location. Furthermore, while sequentiality has been investigated for capacitated facility location games [19] and for games similar to fair cost facility location [25], to the best of our knowledge there is no results concerning the sequential Price of Anarchy or Stability when players have no rules on how to share opening costs.…”

Sequential scheduling on identical machines

“…We study the corresponding sequential price of anarchy of the game, denoted SPoA, which is the costratio of the worst subgame-perfect equilibrium to the optimal makespan, that is: Definition 2.1 (Sequential price of anarchy [11]). …”

“…Consequently, a new line of algorithmic research has been initiated recently, which studies sequential versions of games whose simultaneous counterparts are well-studied. Specifically, in their paper [11], Leme et al define the notion of sequential price of anarchy (SPoA) and analyze it in games of Machine Cost Sharing, of Unrelated Machine Scheduling, and of Consensus and Cut. As in our model, in all of their settings the agents are indexed by their "order of arrival" and they choose their actions sequentially, knowing only the choices made by their predecessors.…”