The Average Tree Solution for Multi-choice Forest Games

In this article we study cooperative multi-choice games with limited cooperation possibilities, represented by an undirected forest on the player set. Players in the game can cooperate if they are connected in the forest. We introduce a new (single-valued) solution concept which is a generalization of the average tree solution defined and characterized by Herings et al. [2008] for TU-games played on a forest. Our solution is characterized by component efficiency, component fairness and independence on the greatest activity level. It belongs to the precore of a restricted multi-choice game whenever the underlying multi-choice game is superadditive and isotone. We also link our solution with the hierarchical outcomes (Demange, 2004) of some particular TU-games played on trees. Finally, we propose two possible economic applications of our average tree solution.Average tree solution; Communication graph; (pre-)Core; Hierarchical outcomes; Multi-choice games.

The Average Tree Solution for Multi-choice Forest Games

In this article we study cooperative multi-choice games with limited cooperation possibilities, represented by an undirected forest on the player set. Players in the game can cooperate if they are connected in the forest. We introduce a new (single-valued) solution concept which is a generalization of the average tree solution defined and characterized by Herings et al. [2008] for TU-games played on a forest. Our solution is characterized by component efficiency, component fairness and independence on the greatest activity level. It belongs to the precore of a restricted multi-choice game whenever the underlying multi-choice game is superadditive and isotone. We also link our solution with the hierarchical outcomes (Demange, 2004) of some particular TU-games played on trees. Finally, we propose two possible economic applications of our average tree solution

MaaSim: A Liveability Simulation for Improving the Quality of Life in Cities

Urbanism is no longer planned on paper thanks to powerful models and 3D simulation platforms. However, current work is not open to the public and lacks an optimisation agent that could help in decision making. This paper describes the creation of an open-source simulation based on an existing Dutch liveability score with a built-in AI module. Features are selected using feature engineering and Random Forests. Then, a modified scoring function is built based on the former liveability classes. The score is predicted using Random Forest for regression and achieved a recall of 0.83 with 10-fold cross-validation. Afterwards, Exploratory Factor Analysis is applied to select the actions present in the model. The resulting indicators are divided into 5 groups, and 12 actions are generated. The performance of four optimisation algorithms is compared, namely NSGA-II, PAES, SPEA2 and eps-MOEA, on three established criteria of quality: cardinality, the spread of the solutions, spacing, and the resulting score and number of turns. Although all four algorithms show different strengths, eps-MOEA is selected to be the most suitable for this problem. Ultimately, the simulation incorporates the model and the selected AI module in a GUI written in the Kivy framework for Python. Tests performed on users show positive responses and encourage further initiatives towards joining technology and public applications.Comment: 16 page