Simple Games on Complex Networks

TL;DR

The paper examines how simple two-team games unfold on four network topologies (REG, ER, BA, GEO), progressing from a fully symmetric game (G1) to strategy-enabled variants (G2–G5). It uses coincidence similarity networks to visualize relationships among 20 configurations (5 games × 4 networks) and to interpret how topology and strategic rules shape outcomes. Key findings show that network topology generally exerts limited influence on victory/tie rates and durations, while strategic rules markedly alter dynamics, with longer durations arising from deterministic strategies and shorter durations when randomness is introduced. The work demonstrates the utility of coincidence similarity networks for uncovering structure in complex dynamical data and points to future studies on modular networks and alternative strategies.

Abstract

The relationship between topology and dynamics of complex systems has motivated continuing interest from the scientific community. In the present work, we address this interesting topic from the perspective of simple games, involving two teams playing according to a small set of simple rules, taking place on four types of complex networks. Starting from a minimalist game, characterized by full symmetry always leading to ties, four other games are described in progressive order of complexity, taking into account the presence of neighbors as well as strategies. Each of these five games, as well as their specific changes when implemented in four types of networks, are studied in terms of statistics of the total duration of the game as well as the number of victories and ties, with several interesting results that substantiate, in some cases, the importance of the network topology on the respective dynamics. As a subsidiary result, the visualization of relationships between the data elements in terms of coincidence similarity networks allowed a more complete and direct interpretation of the obtained results.

Figures (8)

• Figure 1: The coincidence similarity networks, derived from Table \ref{['tab:results']} and using $D=1$, expressing the relationships among the 20 considered configurations of game/type of network labeled according to game types (a) and complex network models (b).
• Figure 2: Summarization of the relative interconnections among the three clusters identified in Fig \ref{['fig:sim_net1']}(a) as a respective coincidence complex network. The intermediate group G3 consists precisely to the game G3 implemented in the four considered topologies.
• Figure 3: The histograms of the duration of the games respectively to the 20 considered cases. The insets indicate the average $\pm$ the standard deviation of the duration times.
• Figure 4: The coincidence similarity network ($D=1$) obtained respectively to the duration of the games taking place in the several considered network topologies with the nodes shown in colors corresponding to the types of games (a) and types of networks (b). In the former case, the types of game G1 led to a well-separated group of nodes, with the nodes corresponding to the type G3 intermediating the connections with the other three types of games.
• Figure 5: The coincidence similarity network ($D=2$) considering the duration of only the games G1, G2, and G5 shown in colors corresponding to the types of games (a) and types of networks (b). Two cases of the game G5 resulted more substantially separated from the remainder of the network.