Nash Equilibria, collusion in games and the coevolutionary particle swarm algorithm

In recent work, we presented a deterministic algorithm to investigate collusion between players in a game where the players’ payoff functions are subject to a variational inequality describing the equilibrium of a transportation system. In investigating the potential for collusion between players, the diagonalization algorithm returned a local optimum. In this paper, we apply a coevolutionary particle swarm optimization (PSO) algorithm developed in earlier research in an attempt to return the global maximum. A numerical experiment is used to verify the performance of the algorithm in overcoming local optimum

Elasticity of demand and highway scheme benefit evaluation

DIADEM (Dynamic Integrated Assignment and Demand Modelling) software package has been recently introduced to complement the variable demand modeling process. The fundamental impetus of DIADEM is to test the robustness of highway scheme benefits and this software package is intended to be complementary to conventional demand modeling software. This paper tests a small hypothetical network of a town in the UK to compare the benefits under the current conventional methodology and under the DIADEM methodology

Differential evolution based bi-level programming algorithm for computing normalized nash equilibrium

The Generalised Nash Equilibrium Problem (GNEP) is a Nash game with the distinct feature that the feasible strategy set of a player depends on the strategies chosen by all her opponents in the game. This characteristic distinguishes the GNEP from a conventional Nash Game. These shared constraints on each player’s decision space, being dependent on decisions of others in the game, increases its computational difficulty. A special solution of the GNEP is the Nash Normalized Equilibrium which can be obtained by transforming the GNEP into a bi-level program with an optimal value of zero in the upper level. In this paper, we propose a Differential Evolution based Bi-Level Programming algorithm embodying Stochastic Ranking to handle constraints (DEBLP-SR) to solve the resulting bi-level programming formulation. Numerical examples of GNEPs drawn from the literature are used to illustrate the performance of the proposed algorithm

Tolling, Capacity Selection and Equilibrium Problems with Equilibrium Constraints

An Equilibrium problem with an equilibrium constraint is a mathematical construct that can be applied to private competition in highway networks. In this paper we consider the problem of finding a Nash Equilibrium regarding competition in toll pricing on a network utilising 2 alternative algorithms. In the first algorithm, we utilise a Gauss Siedel fixed point approach based on the cutting constraint algorithm for toll pricing. In the second algorithm, we extend an existing sequential linear complementarity approach for finding Nash equilibrium subject to Wardrop Equilibrium constraints. Finally we consider how the equilibrium may change between the Nash competitive equilibrium and a collusive equilibrium where the two players co-operate to form the equivalent of a monopoly operation

Solving transportation bi-level programs with differential evolution

Bi-level programming problems arise in situations when the decision maker has to take into account the responses of the users to his decisions. These problems are recognized as one of the most difficult and challenging problems in transportation systems management. Several problems within the transportation literature can be cast in the bi-level programming framework. At the same time, significant advances have been made in the deployment of stochastic heuristics for function optimization. This paper reports on the use of Differential Evolution (DE) for solving bi-level programming problems with applications in the field of transportation planning. After illustrating our solution algorithm with some mathematical functions, we then apply this method to two control problems facing the transportation network manager. DE is integrated with conventional traffic assignment techniques to solve the resulting bi-level program. Numerical computations of this DE based algorithm (known as DEBLP) are presented and compared with existing results. Our numerical results augment the view that DE is a suitable contender for solving these types of problems

Tolling, collusion and equilibrium problems with equilibrium constraints

An Equilibrium Problem with an Equilibrium Constraint (EPEC) is a mathematical construct that can be applied to private competition in highway networks. In this paper we consider the problem of finding a Nash Equilibrium in a situation of competition in toll pricing on a network utilising two alternative algorithms. In the first algorithm, we utilise a Gauss Seidel fixed point approach based on the cutting constraint algorithm for toll pricing. The second algorithm that we propose, a novel contribution of this paper, is the extension of an existing sequential linear complementarity programming approach for finding the competitive Nash equilibrium when there is a lower level equilibrium constraint. Finally we develop an intuitive approach to represent collusion between players and demonstrate that as the level of collusion goes from none to full collusion so the solution maps from the Nash to monopolistic solution. However we also show that there may be local solutions for the collusive monopoly which lie closer to the second best welfare toll solution than does the competitive Nash equilibrium

Ancient Organic Residues as Cultural and Environmental Proxies: The Value of Legacy Objects

Often treated as an accessory science, organic residue analysis (ORA) has the capacity to illuminate otherwise hidden aspects of ancient technology, culture, and economy, and therein can play a central role in archaeological inquiry. Through ORA, both the intact vessel freshly excavated from a tomb and the sherd tucked away in a museum storage closet can offer insights into their contents, their histories, and the cultures that created them—provided the results can be carefully calibrated to account for their treatment during and after excavation. The case study below presents ORA data obtained from a range of artifacts from Late Bronze Age Crete, setting results from freshly-excavated and legacy objects alongside one another. Although legacy objects do tend to yield diminished results from both a quantitative and qualitative perspective, our comparative work has demonstrated both their value and untapped potential when their object biographies are carefully considered. It also sheds light on biomarker degradation processes, which have implications for methodologies of extraction and interpretation of legacy objects. Comparative studies such as these broaden the pool of viable ORA candidates, and therein amplify ORA’s ability to reveal patterns of consumption as well as ecological and environmental change. They also highlight the role and value of data-sharing in collaborative environments such as the OpenARCHEM archaeometric database. Keywords: organic residue analysis (ORA); archaeochemistry; phytochemistry; ethnobotany; ethnohistory; paleoenvironment; paleoecology; legacy artifacts; perfumed oils; Minoan Crete; OpenARCHE

The effect of cotton-based collection methods on eosinophil cationic protein (ECP) concentrations detected in saliva

Teck Yee Wong, David Koh, Andrew Wee, Vivian Ng, Yong Tat Koh, Zhenjie Sum, Gerald KohDepartment of Community, Occupational and Family Medicine, Yong Loo Lin School of Medicine, National University of Singapore, SingaporeBackground: Salivary eosinophil cationic protein (ECP) level has the potential to be an assessment tool for asthma. Its measurement is not well-established and needs standardization. We studied how passive drool (PD) and two commercial devices, Salivette® (cotton-based device) and Sorbette® (cellulose–cotton-based-device), may affect ECP levels during collection among healthy subjects.Methods: Study I (n = 10) involved direct sampling of healthy adult subjects with Salivette® and Sorbette®. Study II (n = 33) involved ‘indirect’ sampling of previously collected PD by both devices.Results: In study I, ECP levels were detected in all PD samples but only in three with Sorbette® and none with Salivette® (collection order: PD, Sorbette® and Salivette®). We changed the order of collection (Salivette®, Sorbette®, PD) and the results were similar (ECP levels detected in all PD samples, three with Sorbette® and only one with Salivette®). In study II, ECP levels in saliva collected by PD was 12.8 μg/L (median) and using Sorbette® and Salivette® were < 2.0 μg/L and 3.4 μg/L respectively (p < 0.01). ECP levels in PD correlated with Sorbette® (rs = 0.79, p < 0.01) and Salivette® (rs = 0.62, p 0.01).Conclusion: Compared to PD, saliva collected using cotton or cellulose-based collection devices resulted in lower measurable ECP levels.Keywords: salivary ECP, collection method