The Role of Monotonicity in the Epistemic Analysis of Strategic Games

It is well-known that in finite strategic games true common belief (or common knowledge) of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. We establish a general theorem that deals with monotonic rationality notions and arbitrary strategic games and allows to strengthen the above result to arbitrary games, other rationality notions, and transfinite iterations of the elimination process. We also clarify what conclusions one can draw for the customary dominance notions that are not monotonic. The main tool is Tarski's Fixpoint Theorem.Comment: 20 page

Proof-theoretic Analysis of Rationality for Strategic Games with Arbitrary Strategy Sets

In the context of strategic games, we provide an axiomatic proof of the statement Common knowledge of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. Rationality here means playing only strategies one believes to be best responses. This involves looking at two formal languages. One is first-order, and is used to formalise optimality conditions, like avoiding strictly dominated strategies, or playing a best response. The other is a modal fixpoint language with expressions for optimality, rationality and belief. Fixpoints are used to form expressions for common belief and for iterated elimination of non-optimal strategies.Comment: 16 pages, Proc. 11th International Workshop on Computational Logic in Multi-Agent Systems (CLIMA XI). To appea

Hubungan Tingkat Pengetahuan Dengan Ketepatan Pemilihan Obat Influenza Pada Mahasiswa Farmasi UMS

Influenza merupakan self limiting disease yang dapat menyerang setiap orang tanpa mengenal usia dan jenis kelamin. Salah satu upaya pengobatan yang paling sering dilakukan untuk mengobati penyakit ini adalah dengan tindakan swamedikasi. Pengetahuan yang baik sangat diperlukan agar tindakan swamedikasi berjalan baik sehingga tecapai tujuan pengobatan yang diinginkan. Tujuan penelitian ini untuk mengetahui hubungan antara tingkat pengetahuan dengan ketepatan pemilihan obat influenza pada mahasiswa Farmasi UMS. Penelitian dilakukan dengan metode cross sectional menggunakan kuesioner terhadap 100 mahasiswa Farmasi yang pernah atau sedang melakukan swamedikasi influenza. Teknik pengambilan sampel menggunakan purposive quota sampling. Analisis data secara deskriptif dilakukan dengan uji chi square. Hasil penelitian katagori baik sekali untuk pengetahuan sebesar 46%, dan baik sebesar 33%. Hasil ketepatan pemilihan obat 76% belum tepat berdasarkan kerasionalannya. Hasil pengujian chi square menunjukkan bahwa tidak ada hubungan antara tingkat pengetahuan mahasiswa Farmasi Universitas Muhammadiyah Surakarta terhadap ketepatan pemilihan obat influenza dengan nilai p = 0,109

‘It’s too late’. Is it really? Considerations for amblyopia treatment in older children

In recent years, media coverage has demonstrated instances in which families of children aged 7 and older, newly diagnosed with strabismic and/or anisometropic amblyopia through community eyecare services, were told it was ‘too late’ for their child to effectively respond to conventional amblyopia treatment (occlusion or atropine penalisation). Formal guidance pertaining to binocular vision anomalies from eyecare professional bodies does not specifically make reference to a child’s age, beyond stating the importance of early diagnosis and treatment of strabismus/amblyopia. However, there have been many changes in the way we view the recovery period for amblyopia, and it is well demonstrated both within literature and clinical practice that conventional treatment can improve amblyopic eye visual acuity in children beyond the age of 7 years. The occurrence of these media described cases within the community eyecare sphere would suggest it is worthwhile revisiting the literature on the subject of amblyopia treatment in older children (aged 7+ years), to address misconceptions and place in the spotlight current considerations facing clinicians when treating newly diagnosed amblyopia within this age group. This perspective review provides an evidence-based update covering the various considerations associated with treatment of amblyopia in older children, along with recent amblyopia treatment advances that could have an impact on treatment prospects for this patient group. Considerations include the risks, benefits and efficacy of treating newly diagnosed amblyopia in older children, monitoring density of suppression to mitigate intractable diplopia risk, and recent findings regarding binocular treatments for amblyopia

Refining Nodes and Edges of State Machines

State machines are hierarchical automata that are widely used to structure complex behavioural specifications. We develop two notions of refinement of state machines, node refinement and edge refinement. We compare the two notions by means of examples and argue that, by adopting simple conventions, they can be combined into one method of refinement. In the combined method, node refinement can be used to develop architectural aspects of a model and edge refinement to develop algorithmic aspects. The two notions of refinement are grounded in previous work. Event-B is used as the foundation for our refinement theory and UML-B state machine refinement influences the style of node refinement. Hence we propose a method with direct proof of state machine refinement avoiding the detour via Event-B that is needed by UML-B

Coalition Resilient Outcomes in Max k-Cut Games

We investigate strong Nash equilibria in the \emph{max $k$-cut game}, where we are given an undirected edge-weighted graph together with a set $\{1,\ldots, k\}$ of $k$ colors. Nodes represent players and edges capture their mutual interests. The strategy set of each player $v$ consists of the $k$ colors. When players select a color they induce a $k$-coloring or simply a coloring. Given a coloring, the \emph{utility} (or \emph{payoff}) of a player $u$ is the sum of the weights of the edges $\{u,v\}$ incident to $u$, such that the color chosen by $u$ is different from the one chosen by $v$. Such games form some of the basic payoff structures in game theory, model lots of real-world scenarios with selfish agents and extend or are related to several fundamental classes of games. Very little is known about the existence of strong equilibria in max $k$-cut games. In this paper we make some steps forward in the comprehension of it. We first show that improving deviations performed by minimal coalitions can cycle, and thus answering negatively the open problem proposed in \cite{DBLP:conf/tamc/GourvesM10}. Next, we turn our attention to unweighted graphs. We first show that any optimal coloring is a 5-SE in this case. Then, we introduce $x$-local strong equilibria, namely colorings that are resilient to deviations by coalitions such that the maximum distance between every pair of nodes in the coalition is at most $x$. We prove that $1$-local strong equilibria always exist. Finally, we show the existence of strong Nash equilibria in several interesting specific scenarios.Comment: A preliminary version of this paper will appear in the proceedings of the 45th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM'19

Efficient Equilibria in Polymatrix Coordination Games

We consider polymatrix coordination games with individual preferences where every player corresponds to a node in a graph who plays with each neighbor a separate bimatrix game with non-negative symmetric payoffs. In this paper, we study $\alpha$-approximate $k$-equilibria of these games, i.e., outcomes where no group of at most $k$ players can deviate such that each member increases his payoff by at least a factor $\alpha$. We prove that for $\alpha \ge 2$ these games have the finite coalitional improvement property (and thus $\alpha$-approximate $k$-equilibria exist), while for $\alpha < 2$ this property does not hold. Further, we derive an almost tight bound of $2\alpha(n-1)/(k-1)$ on the price of anarchy, where $n$ is the number of players; in particular, it scales from unbounded for pure Nash equilibria ($k = 1)$ to $2\alpha$ for strong equilibria ($k = n$). We also settle the complexity of several problems related to the verification and existence of these equilibria. Finally, we investigate natural means to reduce the inefficiency of Nash equilibria. Most promisingly, we show that by fixing the strategies of $k$ players the price of anarchy can be reduced to $n/k$ (and this bound is tight)

Acceptability with general orderings

We present a new approach to termination analysis of logic programs. The essence of the approach is that we make use of general orderings (instead of level mappings), like it is done in transformational approaches to logic program termination analysis, but we apply these orderings directly to the logic program and not to the term-rewrite system obtained through some transformation. We define some variants of acceptability, based on general orderings, and show how they are equivalent to LD-termination. We develop a demand driven, constraint-based approach to verify these acceptability-variants. The advantage of the approach over standard acceptability is that in some cases, where complex level mappings are needed, fairly simple orderings may be easily generated. The advantage over transformational approaches is that it avoids the transformation step all together. {\bf Keywords:} termination analysis, acceptability, orderings.Comment: To appear in "Computational Logic: From Logic Programming into the Future