Nash Equilibria in Games over Graphs Equipped with a Communication Mechanism

We study pure Nash equilibria in infinite-duration games on graphs, with partial visibility of actions but communication (based on a graph) among the players. We show that a simple communication mechanism consisting in reporting the deviator when seeing it and propagating this information is sufficient for characterizing Nash equilibria. We propose an epistemic game construction, which conveniently records important information about the knowledge of the players. With this abstraction, we are able to characterize Nash equilibria which follow the simple communication pattern via winning strategies. We finally discuss the size of the construction, which would allow efficient algorithmic solutions to compute Nash equilibria in the original game

Finite-Memory Strategies in Two-Player Infinite Games

International audienceWe study infinite two-player win/lose games (A,B,W) where A,B are finite and W ⊆ (A×B)^ω. At each round Player 1 and Player 2 concurrently choose one action in A and B, respectively. Player 1 wins iff the generated sequence is in W. Each history h ∈ (A×B)^* induces a game (A,B,W_h) with W_h : = {ρ ∈ (A×B)^ω ∣ h ρ ∈ W}. We show the following: if W is in Δ⁰₂ (for the usual topology), if the inclusion relation induces a well partial order on the W_h’s, and if Player 1 has a winning strategy, then she has a finite-memory winning strategy. Our proof relies on inductive descriptions of set complexity, such as the Hausdorff difference hierarchy of the open sets.Examples in Σ⁰₂ and Π⁰₂ show some tightness of our result. Our result can be translated to games on finite graphs: e.g. finite-memory determinacy of multi-energy games is a direct corollary, whereas it does not follow from recent general results on finite memory strategies

On relevant equilibria in reachability games

We study multiplayer reachability games played on a finite directed graph equipped with target sets, one for each player. In those reachability games, it is known that there always exists a Nash equilibrium. But sometimes several equilibria may coexist. For instance we can have two equilibria: a first one where no player reaches his target set and an other one where all the players reach their target set. It is thus very natural to identify “relevant” equilibria. In this paper, we consider different notions of relevant Nash equilibria including Pareto optimal equilibria and equilibria with high social welfare. We also study relevant subgame perfect equilibria in reachability games. We provide complexity results for various related decision problems for both Nash equilibria and subgame perfect equilibria.SCOPUS: ar.jDecretOANoAutActifinfo:eu-repo/semantics/publishe

Prophylactic biological mesh reinforcement versus standard closure of stoma site (ROCSS): a multicentre, randomised controlled trial

Background: Closure of an abdominal stoma, a common elective operation, is associated with frequent complications; one of the commonest and impactful is incisional hernia formation. We aimed to investigate whether biological mesh (collagen tissue matrix) can safely reduce the incidence of incisional hernias at the stoma closure site. Methods: In this randomised controlled trial (ROCSS) done in 37 hospitals across three European countries (35 UK, one Denmark, one Netherlands), patients aged 18 years or older undergoing elective ileostomy or colostomy closure were randomly assigned using a computer-based algorithm in a 1:1 ratio to either biological mesh reinforcement or closure with sutures alone (control). Training in the novel technique was standardised across hospitals. Patients and outcome assessors were masked to treatment allocation. The primary outcome measure was occurrence of clinically detectable hernia 2 years after randomisation (intention to treat). A sample size of 790 patients was required to identify a 40% reduction (25% to 15%), with 90% power (15% drop-out rate). This study is registered with ClinicalTrials.gov, NCT02238964. Findings: Between Nov 28, 2012, and Nov 11, 2015, of 1286 screened patients, 790 were randomly assigned. 394 (50%) patients were randomly assigned to mesh closure and 396 (50%) to standard closure. In the mesh group, 373 (95%) of 394 patients successfully received mesh and in the control group, three patients received mesh. The clinically detectable hernia rate, the primary outcome, at 2 years was 12% (39 of 323) in the mesh group and 20% (64 of 327) in the control group (adjusted relative risk [RR] 0·62, 95% CI 0·43–0·90; p=0·012). In 455 patients for whom 1 year postoperative CT scans were available, there was a lower radiologically defined hernia rate in mesh versus control groups (20 [9%] of 229 vs 47 [21%] of 226, adjusted RR 0·42, 95% CI 0·26–0·69; p<0·001). There was also a reduction in symptomatic hernia (16%, 52 of 329 vs 19%, 64 of 331; adjusted relative risk 0·83, 0·60–1·16; p=0·29) and surgical reintervention (12%, 42 of 344 vs 16%, 54 of 346: adjusted relative risk 0·78, 0·54–1·13; p=0·19) at 2 years, but this result did not reach statistical significance. No significant differences were seen in wound infection rate, seroma rate, quality of life, pain scores, or serious adverse events. Interpretation: Reinforcement of the abdominal wall with a biological mesh at the time of stoma closure reduced clinically detectable incisional hernia within 24 months of surgery and with an acceptable safety profile. The results of this study support the use of biological mesh in stoma closure site reinforcement to reduce the early formation of incisional hernias. Funding: National Institute for Health Research Research for Patient Benefit and Allergan