A Mathematical Representation of "Excitement" in Games from the Viewpoint of a Neutral Audience

Researchers have long believed the concept of "excitement" in games to be subjective and difficult to measure. This paper presents the development of a mathematically computable index that measures this concept from the viewpoint of an audience. One of the key aspects of the index is the differential of the probability of "winning" before and after one specific "play" in a given game. If the probability of winning becomes very positive or negative by that play, then the audience will feel the game to be "exciting." The index makes a large contribution to the study of games and enables researchers to compare and analyze the "excitement" of various games. It may be applied to many fields especially the area of welfare economics, ranging from allocative efficiency to axioms of justice and equity.

A Mathematical Representation of "Excitement" in Games: A Contribution to the Theory of Game Systems

Researchers have long believed the concept of "excitement" in games to be subjective and difficult to measure. This paper presents the development of a mathematically computable index that measures the concept from the viewpoint of an audience and from that of a player. One of the key aspects of the index is the differential of the probability of "winning" before and after one specific "play" in a given game. The index makes a large contribution to the study of games and enables researchers to compare and analyze the “excitement” of various games. It may be applied in many fields, especially the area of welfare economics, and applications may range from those related to allocative efficiency to axioms of justice and equity.

Some notes on the spatial representations

There are conventional methods to calculate the centroid of spatial units and distance among them with using Geographical Information Systems (GIS). The paper points out potential measurement errors of this calculation. By taking Indian district data as an example, systematic errors concealed in such variables are shown. Two comparisons are examined; firstly, we compare the centroid obtained from the spatial units, polygons, and the centre of each city where its district headquarters locates. Secondly, between the centres represented in the above, we calculate the direct distances and road distances obtained from each pair of two districts. From the comparison between the direct distances of centroid of spatial units and the road distances of centre of district headquarters, we show the distribution of errors and list some caveats for the use of conventional variables obtained from GIS.