In randomized algorithms, replacing atomic shared objects with linearizable [1] implementations may affect probability distributions over outcomes [2]. To avoid this problem in the adaptive adversary model, it is necessary and sufficient that implemented objects satisfy strong linearizability [2]. In this paper we study the existence of strongly linearizable implementations from multi-writer registers. We prove the impossibility of wait-free strongly linearizable implementations for a number of standard objects, including snapshots, counters, and max-registers, all of which have wait-free linearizable implementations. To do so, we introduce a new notion of group valency that is useful to analyze (strongly linearizable) implementations from registers. Furthermore, we show that many objects, including snapshots, do have lock-free strongly linearizable implementations. These results separate lock-freedom from wait-freedom under strong linearizability. Proof. For the purpose of a contradiction assume that H is writers-closed. By Lemma10 there is an integer x ≥ 0 such that W(H) = {x}. Then there is a
The problem of reliably transferring data from a set of NP producers to a set of NC consumers in the BAR model, named N-party BAR Transfer (NBART), is an important building block for volunteer computing systems. An algorithm to solve this problem in synchronous systems, which provides a Nash equilibrium, has been presented in previous work. In this paper, we propose an NBART algorithm for asynchronous systems. Furthermore, we also address the possibility of collusion among the Rational processes. Our game theoretic analysis shows that the proposed algorithm tolerates certain degree of arbitrary collusion, while still fulfilling the NBART properties.follow. This concept was later applied to virus inoculation games [5]. In [6], the authors discuss the limitations imposed by regret freedom on communication games, by proving that there are no non-trivial equilibria that provide regret-freedom strategies. Then, they propose a different approach named regret-braving where players are willing to obey the specified solutions basing on their expectations about the environment, and these strategies are regret-free as long as those expectations hold. In our work, we consider that players are risk-averse, that is, they always hold the expectation that Byzantine players will follow the worst possible strategy to their utility.In practice, rational players can seek maximising their utility function by colluding with other players, i.e., forming coalitions. Therefore, the solution concepts are more robust if they account for such rational behaviour. Aumann [7] addressed this issue by defining an equilibrium as a profile of strategies where no deviating collusion strategy provides a greater utility for all players of the group. Then, Bernheim et. al. [8] introduced the notion of coalition-proof Nash equilibrium, where no deviations by a coalition can perform better, although they do not allow further deviations to the collusion strategy. This work was later extended to take into consideration correlated strategies [9].The work of [10] considered the existence of processes with unexpected utilities and collusion. The authors proposed the solution concept of (k, t)-robustness, where no process can increase its utility by deviating in collusion with up to k − 1 other processes, regardless of the Byzantine behaviour of up to t processes. This notion is stronger than the previous models for collusion, since it accounts for arbitrary collusion where it should be true that no player performs better by deviating from the equilibrium strategy, even if that implies decreasing the utility of other players within the coalition. Unfortunately, in certain scenarios such as communication games (where players incur communication costs), it was shown that no game can be (k, t)-robust for k, t > 0 [11].Additional literature relevant to our results include works on agreement in the BAR model [2,11] and data dissemination [12,13,14], which studied protocols tolerant to the BAR model and showed in which conditions those solutions provide Nash equili...
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