On Markov Games Played by Bayesian and Boundedly-Rational Players

We present a new game-theoretic framework in which Bayesian players with bounded rationality engage in a Markov game and each has private but incomplete information regarding other players' types. Instead of utilizing Harsanyi's abstract types and a common prior, we construct intentional player types whose structure is explicit and induces a {\em finite-level} belief hierarchy. We characterize an equilibrium in this game and establish the conditions for existence of the equilibrium. The computation of finding such equilibria is formalized as a constraint satisfaction problem and its effectiveness is demonstrated on two cooperative domains

Team behavior in interactive dynamic influence diagrams with applications to ad hoc teams

Planning for ad hoc teamwork is challenging because it involves agents collaborating without any prior coordination or communication. The focus is on principled methods for a single agent to cooperate with others. This motivates investigating the ad hoc teamwork problem in the context of individual decision making frameworks. However, individual decision making in multiagent settings faces the task of having to reason about other agents' actions, which in turn involves reasoning about others. An established approximation that operationalizes this approach is to bound the infinite nesting from below by introducing level 0 models. We show that a consequence of the finitely-nested modeling is that we may not obtain optimal team solutions in cooperative settings. We address this limitation by including models at level 0 whose solutions involve learning. We demonstrate that the learning integrated into planning in the context of interactive dynamic influence diagrams facilitates optimal team behavior, and is applicable to ad hoc teamwork.Comment: 8 pages, Appeared in the MSDM Workshop at AAMAS 2014, Extended Abstract version appeared at AAMAS 2014, Franc

Can bounded and self-interested agents be teammates? Application to planning in ad hoc teams

Planning for ad hoc teamwork is challenging because it involves agents collaborating without any prior coordination or communication. The focus is on principled methods for a single agent to cooperate with others. This motivates investigating the ad hoc teamwork problem in the context of self-interested decision-making frameworks. Agents engaged in individual decision making in multiagent settings face the task of having to reason about other agents’ actions, which may in turn involve reasoning about others. An established approximation that operationalizes this approach is to bound the infinite nesting from below by introducing level 0 models. For the purposes of this study, individual, self-interested decision making in multiagent settings is modeled using interactive dynamic influence diagrams (I-DID). These are graphical models with the benefit that they naturally offer a factored representation of the problem, allowing agents to ascribe dynamic models to others and reason about them. We demonstrate that an implication of bounded, finitely-nested reasoning by a self-interested agent is that we may not obtain optimal team solutions in cooperative settings, if it is part of a team. We address this limitation by including models at level 0 whose solutions involve reinforcement learning. We show how the learning is integrated into planning in the context of I-DIDs. This facilitates optimal teammate behavior, and we demonstrate its applicability to ad hoc teamwork on several problem domains and configurations

Predictors of mortality among hospitalized COVID-19 patients and risk score formulation for prioritizing tertiary care—An experience from South India

BACKGROUND: We retrospectively data-mined the case records of Reverse Transcription Polymerase Chain Reaction (RT-PCR) confirmed COVID-19 patients hospitalized to a tertiary care centre to derive mortality predictors and formulate a risk score, for prioritizing admission. METHODS AND FINDINGS: Data on clinical manifestations, comorbidities, vital signs, and basic lab investigations collected as part of routine medical management at admission to a COVID-19 tertiary care centre in Chengalpattu, South India between May and November 2020 were retrospectively analysed to ascertain predictors of mortality in the univariate analysis using their relative difference in distribution among ‘survivors’ and ‘non-survivors’. The regression coefficients of those factors remaining significant in the multivariable logistic regression were utilised for risk score formulation and validated in 1000 bootstrap datasets. Among 746 COVID-19 patients hospitalised [487 “survivors” and 259 “non-survivors” (deaths)], there was a slight male predilection [62.5%, (466/746)], with a higher mortality rate observed among 40–70 years age group [59.1%, (441/746)] and highest among diabetic patients with elevated urea levels [65.4% (68/104)]. The adjusted odds ratios of factors [OR (95% CI)] significant in the multivariable logistic regression were SaO(2)3; 3.01 (1.61–5.83), Age ≥50 years;2.52 (1.45–4.43), Pulse Rate ≥100/min: 2.02 (1.19–3.47) and coexisting Diabetes Mellitus; 1.73 (1.02–2.95) with hypertension and gender not retaining their significance. The individual risk scores for SaO(2)3–11, Age ≥50 years-9, Pulse Rate ≥100/min-7 and coexisting diabetes mellitus-6, acronymed collectively as ‘OUR-ARDs score’ showed that the sum of scores ≥ 25 predicted mortality with a sensitivity-90%, specificity-64% and AUC of 0.85. CONCLUSIONS: The ‘OUR ARDs’ risk score, derived from easily assessable factors predicting mortality, offered a tangible solution for prioritizing admission to COVID-19 tertiary care centre, that enhanced patient care but without unduly straining the health system

Bayesian Markov Games with Explicit Finite-Level Types

In impromptu or ad hoc settings, participating players are precluded from precoordination. Subsequently, each player's own model is private and includes some uncertainty about the others' types or behaviors. Harsanyi's formulation of a Bayesian game lays emphasis on this uncertainty while the players each play exactly one turn. We propose a new game-theoretic framework where Bayesian players engage in a Markov game and each has private but imperfect information regarding other players' types. Consequently, we construct player types whose structure is explicit and includes a finite level belief hierarchy instead of utilizing Harsanyi's abstract types and a common prior distribution. We formalize this new framework and demonstrate its effectiveness on two standard ad hoc teamwork domains involving two or more ad hoc players