Efficient Local Search in Coordination Games on Graphs

We study strategic games on weighted directed graphs, where the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy augmented by a fixed non-negative bonus for picking a given strategy. These games capture the idea of coordination in the absence of globally common strategies. Prior work shows that the problem of determining the existence of a pure Nash equilibrium for these games is NP-complete already for graphs with all weights equal to one and no bonuses. However, for several classes of graphs (e.g. DAGs and cliques) pure Nash equilibria or even strong equilibria always exist and can be found by simply following a particular improvement or coalition-improvement path, respectively. In this paper we identify several natural classes of graphs for which a finite improvement or coalition-improvement path of polynomial length always exists, and, as a consequence, a Nash equilibrium or strong equilibrium in them can be found in polynomial time. We also argue that these results are optimal in the sense that in natural generalisations of these classes of graphs, a pure Nash equilibrium may not even exist.Comment: Extended version of a paper accepted to IJCAI1

Choosing Products in Social Networks

We study the consequences of adopting products by agents who form a social network. To this end we use the threshold model introduced in Apt and Markakis, arXiv:1105.2434, in which the nodes influenced by their neighbours can adopt one out of several alternatives, and associate with such each social network a strategic game between the agents. The possibility of not choosing any product results in two special types of (pure) Nash equilibria. We show that such games may have no Nash equilibrium and that determining the existence of a Nash equilibrium, also of a special type, is NP-complete. The situation changes when the underlying graph of the social network is a DAG, a simple cycle, or has no source nodes. For these three classes we determine the complexity of establishing whether a (special type of) Nash equilibrium exists. We also clarify for these categories of games the status and the complexity of the finite improvement property (FIP). Further, we introduce a new property of the uniform FIP which is satisfied when the underlying graph is a simple cycle, but determining it is co-NP-hard in the general case and also when the underlying graph has no source nodes. The latter complexity results also hold for verifying the property of being a weakly acyclic game.Comment: 15 pages. Appeared in Proc. of the 8th International Workshop on Internet and Network Economics (WINE 2012), Lecture Notes in Computer Science 7695, Springer, pp. 100-11

Paradoxes in Social Networks with Multiple Products

Recently, we introduced in arXiv:1105.2434 a model for product adoption in social networks with multiple products, where the agents, influenced by their neighbours, can adopt one out of several alternatives. We identify and analyze here four types of paradoxes that can arise in these networks. To this end, we use social network games that we recently introduced in arxiv:1202.2209. These paradoxes shed light on possible inefficiencies arising when one modifies the sets of products available to the agents forming a social network. One of the paradoxes corresponds to the well-known Braess paradox in congestion games and shows that by adding more choices to a node, the network may end up in a situation that is worse for everybody. We exhibit a dual version of this, where removing available choices from someone can eventually make everybody better off. The other paradoxes that we identify show that by adding or removing a product from the choice set of some node may lead to permanent instability. Finally, we also identify conditions under which some of these paradoxes cannot arise.Comment: 22 page

Nash Equilibrium in Generalised Muller Games

We suggest that extending Muller games with preference ordering for players is a natural way to reason about unbounded duration games. In this context, we look at the standard solution concept of Nash equilibrium for non-zero sum games. We show that Nash equilibria always exists for such generalised Muller games on finite graphs and present a procedure to compute an equilibrium strategy profile. We also give a procedure to compute a subgame perfect equilibrium when it exists in such games

Constrained Pure Nash Equilibria in Polymatrix Games

We study the problem of checking for the existence of constrained pure Nash equilibria in a subclass of polymatrix games defined on weighted directed graphs. The payoff of a player is defined as the sum of nonnegative rational weights on incoming edges from players who picked the same strategy augmented by a fixed integer bonus for picking a given strategy. These games capture the idea of coordination within a local neighbourhood in the absence of globally common strategies. We study the decision problem of checking whether a given set of strategy choices for a subset of the players is consistent with some pure Nash equilibrium or, alternatively, with all pure Nash equilibria. We identify the most natural tractable cases and show NP or coNP-completness of these problems already for unweighted DAGs.Comment: Extended version of a paper accepted to AAAI1

A review of maternal and fetal outcome of induction of labour with Foley’s catheter and extra amniotic saline infusion in women with previous caesarean delivery

Background: Incidence of induction of labour has increased in the recent past due to increased screening facilities like ante partum fetal surveillance. Vaginal birth after caesarean section (VBAC) is one of the strategies developed to control the rising rate of caesarean sections. Intracervical Foley’s catheter reduces the risk of uterus hyper tonicity and rupture in women with one caesarean section as it’s placement induces the cervical repining without inducing any uterine contractions.Methods: A prospective study of 35 women with one previous LCSs, term gestation and singleton pregnancy, were selected for trial of labour (TOL) considering inclusion and exclusion criteria.Results: Out of 35 cases studied 21 cases (60%) went for successful induction with Foleys and the remaining 40% underwent caesarean section. The mean time interval for Foley’s expulsion was 6.74 in the success group and 10.04 in the failed group (p value <0.05). In 4 cases there were meconium stained liquor, and they underwent emergency LSCS. One case (2.8%) had scar rupture which also underwent caesarean section.Conclusions: This study shows that the Foley catheter is an effective method of cervical ripening with additional benefit of low cost, reversibility, easy availability and lack of need for special storage. This method confers significant improvement in Bishop Score and vaginal delivery was achieved in majority of patients