CC BY
0
TOPOLOGICAL ASPECTS OF COOPERATION STRATEGIES (AFRICAN
COUNTRIES CASE)
Sikiru Saheed Abayomi, Graduate Student
A.I. Trufanov, Candidate of Physical and Mathematical Sciences, Associate Professor Irkutsk National Research Technical University (Russia, Irkutsk)
DOI:10.24412/2500-1000-2024-5-3-273-280
Abstract. The availability of the World Wide Web has made businesses grow beyond the local geographical limits so that businesses can now cooperation deeds with partners within other regions or states both. This makes this research a vital tool for associations of national and international organizations which are looking into cooperating while creating and providing such strategies and politics. The primary objective of this research is to investigate the structural factors that drive or impede cooperation among organizations and the strategies that can be employed to enhance the effectiveness of cooperative networks, with a particular focus to the starting cooperation positions and their dynamics in the processes on complex networks. This study employed agent-based modeling and simulations of the Prisoner's Dilemma and Stag-Hunt games on complex networks representing African trade relationships. The networks used in the simulations included synthetic topologies (Kleinberg, Erdos-Renyi, Barabasi-Albert) and an empirical network based on actual trade connections between African countries. The results suggest that the initial proportion of cooperators and the network topology significantly influenced the evolution of cooperation and the overall network effectiveness. For instance, higher initial proportions of cooperators led to higher final average percentages and higher average payoffs per node, moreover, the dynamics of these values on the network of African trade relations significantly differbi from that on synthetic networks.
Keywords: regional/state partnerships, cooperation models, prisoner S dilemma, payoff matrix, complex networks, topologies, dynamics of cooperation
1. Introduction
Cooperation among organizations and nations is essential for achieving collective goals and creating value. However, the inherent unpredictability of human behavior within these cooperative networks can pose significant challenges. This research aims to investigate the factors that drive or impede cooperation among African countries in trade relationships and the strategies that can be employed to enhance the effectiveness of these cooperative networks.
The relevance of this study lies in its potential to guide organizations and policymakers in navigating the complexities of cooperative efforts, particularly within the context of African trade relationships.
Through an interdisciplinary approach and instruments of contemporary Network Science [1] that integrates complex systems analysis, game theory, and agent-based modeling, this study seeks to contribute to the
knowledge of cooperative networks and provide valuable insights for fostering economic integration, regional development, and sustainable trade relationships among African nations.
2. Trades within African countries
Various factors, including political relationships, alliances, and resource availability, have shaped trade within African countries. Understanding the dynamics of trade flows among African nations is crucial for promoting economic growth and fostering regional cooperation.
- Political Relationships and Trade Volumes: It has been observed that most countries tend to supply more goods to countries with which they have friendly political ties [2]. This phenomenon highlights the influence of diplomatic relations on trade patterns, as nations are more inclined to engage in economic exchanges with allies and partners.
- Alliances and High Trade Volumes: Countries that are part of regional or economic alliances tend to exhibit higher trade volumes among themselves [3]. These alliances facilitate trade agreements, reduce tariffs, and promote economic integration, fostering increased trade flows within the bloc.
- Lack of Interlocking and Trade Imbalances: Countries with low levels of contact and interlocking relationships with other African nations tend to receive lower import volumes [4]. This phenomenon suggests that geographic proximity, cultural ties, and established trade routes significantly shape trade patterns within the continent.
- Resource Availability and Trade Flows: Countries experiencing famine or food shortages due to low domestic supplies often limit their exports to other nations [5]. This situation arises as nations prioritize meeting their internal food demands before engaging in substantial trade with other countries.
- Cooperation and Trade Expansion: Countries actively participate in cooperative frameworks with multiple African partners tend to send out more supplies and receive more imports [4]. This observation highlights the positive impact of regional cooperation on trade flows, as nations that foster collaborative relationships are better positioned to leverage their comparative advantages and access larger markets.
It is important to note that trade within African countries is not solely determined by a single factor but rather by a complex interplay of political, economic, and social dynamics. By understanding these underlying patterns and drivers, policymakers and stakeholders can develop strategies to promote sustainable trade relationships, foster economic integration, and address regional trade imbalances.
Comprehensive research in this area can provide valuable insights into the challenges and opportunities associated with intra-African trade, ultimately contributing to the continent's economic development and regional integration efforts.
3. Models of cooperation games on networks
This study employs a quantitative approach, utilizing agent-based modeling and simulations to investigate cooperation dynamics and network effectiveness within African trade networks. The primary focus is modeling the Prisoner's Dilemma (PD) - like games on complex networks representative of African countries' trade relationships.
General methodology.
The Prisoner's Dilemma (PD) game and the Stag-Hunt game are well-established mathematical models [6-9]. Both games are represented by pertinent Payoff matrices [10] (fig. 1).
Player 2
Cooperate Defect
Player 1 Cooperate N. 2 \r l \ N. 2 Xt s\ 1 \
Defect \ 2 \s t\ 1 \ \ 2 \p p\ 1
Fig. 1. Payoff matrix
Where: C = cooperators D = Defectors
- "R" is the payoff for each actor if they cooperate both (CC outcome).
- "S" is the payoff for the cooperator when playing against defector (CD outcome).
- "T" is the payoff for the defector when playing against cooperator (DC outcome).
-"P" is the payoff for each actor if they defect both (DD outcome)
a) Cooperate-Cooperate (CC): The payoff for both players when cooperating.
b) Cooperate-Defect (CD): The payoff for the defector when the cooperator cooperates and for the cooperator when the defector defects.
c) Defect-Cooperate (DC): The payoff for the cooperator when the defector cooperates and the payoff for the defector when the co-operator defects.
d) Defect-Defect (DD): The payoff for both players when they defect.
The PD game models the tension between individual and collective interests, while the Stag-Hunt game explores the trade-off between risk and cooperation.
Games on networks.
Cooperation and decision-making dynamics among individuals or entities within a network structure are of crucial interest. In games, each player has a set of choices, and the payoffs depend on the decisions of connected players.
Several studies were performed for PD game on complex networks [11]. Mostly they focused on behaviour of actors while proportion of cooperators versus defectors changes. Usually synthetic random (Erdos-Renyi), ER and scale-free (Barabasi-Albert), BA topologies were utilized to compose a network background and to compare impact of structural properties on the processes. In [12] memory effect for actors was taken into consideration and it was shown on three topologies ( ER, BA, and degree-degree correlation based ones) that this very effect mitigate the structural impact.
Original model.
Complex networks represent the trade relationships among African countries, capturing the non-uniform nature of these connections.
Agent-based modeling techniques simulate the PD and Stag-Hunt games on these com-
plex networks. Agents representing African countries are assigned initial strategies (cooperate or defect). They can interact and update their strategies based on the payoffs received from their interactions with neighboring agents in the network.
The data analysis process involves several steps:
- Data preprocessing: Cleaning, formatting, and integrating the data from different sources to ensure consistency and compatibility for analysis.
- Agent-based modeling: Implementing agent-based models to simulate the Prisoner's Dilemma (PD) and Stag-Hunt games on the constructed networks, using the node-level attributes from the "Node data" file.
- Network construction: Building complex networks representative of African trade relationships using the "Edge data " file, with nodes representing countries and edges representing trade connections.
- Simulation experiments: Conduct extensive simulations under various scenarios, varying the initial proportion of cooperators, payoff matrices, and network topologies, to explore the cooperation dynamics and network effectiveness.
- Statistical analysis: Applying statistical techniques to analyze the simulation results, identifying patterns, trends, and relationships between input parameters (e.g., initial proportion of cooperators, network topology) and outcome variables - portion of coopera-tors(Y1) and payoff per node (Y2).
- Sensitivity analysis: Performing sensitivity analyses to assess the robustness of the findings and explore the impact of varying model parameters and assumptions on cooperation dynamics and network effectiveness.
4. Data
The data utilized in our research was sourced from publicly available resources such as Kaggle, Google's Open Data, Amazon Web Services, Data.gov, and TRADING ECONOMICS resource [13] among others. The intricate web of African economic ties extends far beyond geographical proximity, shaped by the nuanced interplay of political kinships, resource endowments, and strategic partnerships. Diplomatic bonds hold sway, with nations fostering robust trade flows
among geopolitical allies, underscoring the profound impact of bilateral and multilateral relations. However, regional economic blocs act as catalysts, reducing barriers and unlocking opportunities for nations to leverage their unique strengths across larger markets, weaving an interdependent tapestry. Furthermore, resource scarcities can shift priorities, with
nations grappling with climatic adversities or internal constraints inclined to meet domestic demands before engaging in cross-border trade. This delicate balance between self-sufficiency and integration highlights the multifaceted forces sculpting Africa's dynamic economic landscape.
Fig. 2. Geolocation of African countries: diameters of nodes reflect country' populations
Fig. 3. Network of pairwise trade links between African countries (for trade volume threshold of
$350M)
The data analysis investigates the cooperation dynamics and effectiveness within African trade networks. The primary data sources utilized in this study are the "Node data" (reflected on fig. 4) and "Edge data" (portrayed on fig. 5) files, which contain information about node attributes and trade relationships for African countries, respectively.
The "Node data" file contains information about individual African countries, such as their labels, geographical coordinates, population, and trade volumes within Africa. These node-level attributes contribute to a more comprehensive understanding of the trade dynamics and potential factors influencing cooperation and network effectiveness.
The "Edge data" file provides details on the trade connections between countries, including the source and target nodes, various trade-related metrics (e.g., Stochastic MultiAgent Verification, work in process, over_time, incentive, no_of_workers), and the trade volumes between the connected nodes. This data is the basis for constructing the complex networks representing African trade relationships. To compose the network based on the "Edge data" file the threshold of $350M was chosen for trade volumes (links with lesser volume are not take into account). This "real" network formed a data set along with "synthetic" ones represented by Kleinberg (K), Erdos-Renyi (ER), Barabasi-Albert (BA) topologies for our further simulation processes.
5. Findings
We realized Prisoner's Dilemma and Stag-Hunt games on cooperation and trade out-
comes. Pairwise payoff values were set: R=1, T=1.5, S=0, P=0.1 and R=1., T= 1.25, S=0.25, P=0.75 for these two games, respectively. The analysis reveals that the specific payoff matrices used in the simulations significantly influence the cooperation dynamics and trade effectiveness within African trade networks. Certain payoff configurations, characterized by higher rewards for cooperation and lower temptations to defect, tend to promote more stable and robust cooperation over time.
The simulations are conducted under various scenarios, varying the initial proportion of cooperators, the payoff matrices, and the network topologies. The primary outcome variables of interest are the final average percentage of cooperators (Y1) and the final average payoff per node (Y2), which serve as indicators of cooperation dynamics and network effectiveness, respectively.
The quantitative data obtained from the simulations are analyzed using statistical techniques to identify patterns, trends, and relationships between the input parameters (e.g., the initial proportion of cooperators, network topology) and the outcome variables (Y1 and Y2). The fig. 4 and fig. 5 demonstrate preliminary simulation results for the Stag-Hunt game on various network topologies, including Kleinberg (K), Erdos-Renyi (ER), Barabasi-Albert (BA), and the African countries trade network (A). These results include the final average percentage of coop-erators (Y1) and the final average payoff per node (Y2) for different initial proportions of cooperators.
Fig. 4. Final average percentage of cooperators vs initial one for different topologies. Number of
game iterations is 10
Fig. 5. Final average payoff per node vs initial percentage of cooperators for different topologies.
Number of game iterations is 10
It should be noted that Y1 behavior for A toplogy is close to that for K one, while Y2 dependence for A structure is more similar to that of ER. Scale-free topology (BA) [14] might be considered as a destination for structural organization of real trade networks which proposes better outcome in terms of cooperation and payoff as well.
By combining agent-based modeling, complex network analysis, and simulations of cooperation games, this study aims to contribute to a deeper understanding of the factors that drive cooperation among African countries in trade networks and the strategies
that can be employed to enhance the effectiveness of these cooperative networks.
Interestingly, the node-level attributes, such as population size and trade volumes, play a crucial role in shaping the cooperation behavior of individual nations. Countries with larger populations and higher trade volumes exhibit a greater propensity for cooperative strategies, potentially driven by the desire to maintain stable trade relationships and access larger markets.
6. Conclusion
The results indicate that the initial proportion of cooperators and the network topology
significantly impact the evolution of coopera- can enhance the effectiveness of cooperative tion and overall network performance. Higher trade networks among African nations. Fac-initial proportions of cooperators generally tors such as fostering initial cooperative lead to more effective cooperation dynamics tendencies, optimizing network structures, and network performance. Thorough analysis and tailoring payoff incentives emerge as poof economic connections between African tential levers for promoting stable and mutu-countries provided possibility to compose a ally beneficial trade relationships. unique real trade network for the continent. By combining insights from game theory,
Another specificity of the current study was complex network analysis, and agent-based in its focus on Stag Hunt game which is in modeling, this study offers a multidisciplinary better line with trade connections rather than approach to optimizing the effectiveness of regular Prisoner's dilemma one. Comparison cooperative networks in real-world scenarios. of the results of the game for diverse synthet- Moving forward, further research is need-
ic and real topology is a novelty. ed to explore the practical implementation of
The analysis of the underlying mecha- the proposed strategies and to assess their im-nisms governing cooperation dynamics in pact on trade flows, economic integration, complex networks offers valuable insights for and regional development within the African proposing practical strategies and policies that continent.
References
1. Vespignani A.Twenty years of network science // Nature. - 2018. - V. 558. - P. 528-529. DOI: 10.1038/d41586-018-05444-y.
2. Geda A., Kebret H. Regional economic integration in Africa: A review of problems and prospects with a case study of COMESA // Journal of African Economies. - 2008. - № 17 (3). -P. 357-394. DOI: 10.1093/jae/ejm021.
3. Yang Y., Gupta S., Regional trade arrangements in Africa: Past performance and the way forward. // African Development Review. - 2007. - № 19 (3). - P. 399-431. DOI: 10.5465/3069440.
4. Bouet A., Laborde Debucquet D., Dienesch E., The costs, and benefits of duty-free, quota-free market access for poor countries: Who and what matters // Journal of Globalization and Development. - 2010. - № 3(1). - P. 1-29. - URL: https://www. cgdev.org/sites/default/files/1423986_file_Bouet_et_al_DFQF_FINAL.pdf_(Accessed: 23.05.2024).
5. Mkandawire P. T., Food insecurity, food prices, and trade: An empirical investigation. // Journal of African Trade. - 2017. - № 4 (1-2). - P. 93-107. DOI: 10.5465/3069440.
6. Hindriks F., Guala F. Institutions, rules, and equilibria: a unified theory // Journal of Institutional Economics. - 2014. - № 11(03). - P. 459-480. DOI: 10.1017/s1744137414000496.
7. Nowak M.A., Bonhoeffer S., May R.M. Spatial Games and the Maintenance of Cooperation// Int. J. Bifurcation Chaos. - 1994. - № 4. - P. 33-56.
8. He Z., Shen C., Shi L., Tanimoto J. Impact of Committed Minorities: Unveiling Critical Mass of Cooperation in the Iterated Prisoner's Dilemma Game. arXiv:2307.08502 [physics. Soc-ph]. - 2023. - 12 p. - URL: https://arxiv.org/pdf/2307.08502_(Accessed: 23.05.2024).
9. You T., Yang H., Wang J., Zhang P., Chen J., Zhang Y. Cooperative behavior under the influence of multiple experienced guides in Prisoner's dilemma game, Applied Mathematics and Computation, Elsevier. - 2023. - V. 458 (C). - DOI: 10.1016/j.amc.2023.128234.
10. Poncela J., Gomez-Gardenes J., Floria L.M., Moreno Y. Robustness of cooperation in the evolutionary prisoner's dilemma on complex networks // New Journal of Physics. - 2007. -№ 9 (6). - P. 184-184. - URL: https://iopscience.iop.org/article/10.1088/1367-2630/9/6/184 (Accessed: 23.05.2024).
11. Wei N., Xie W.-J., Zhou W.-X., The performance of cooperation strategies for enhancing the efficiency of international oil trade networks// Journal of Complex Networks. - 2022. - V. 10, №1. cnab053. doi:10.1093/comnet/cnab053.
12. Lotfi N., Rodrigues F.A. On the effect of memory. On the Prisoner's Dilemma game in correlated networks. arXiv:2206.02522 [physics. Soc-ph]. 2022. - 11 p. URL: https://arxiv.org/pdf/2206.02522_(Accessed: 23.05.2024).
13. TRADING ECONOMICS . Indicators. - URL: https://tradingeconomics.com/countries (Accessed: 25.05.2024).
14. Barabási A.-L., Albert, R. Emergence of scaling in random networks. //Science. - 1999. -V. 286 (5439). - P. 509-512. - DOI:10.1126/science.286.5439.509.
ТОПОЛОГИЧЕСКИЕ АСПЕКТЫ СТРАТЕГИЙ СОТРУДНИЧЕСТВА (ПРИМЕР СТРАН АФРИКАНСКОГО КОНТИНЕНТА)
Сикиру Сахид Абайоми, магистрант А.И. Труфанов, канд. физ.-мат. наук, доцент
Иркутский национальный исследовательский технический университет (Россия, г. Иркутск)
Аннотация. Доступность Всемирной паутины привела к тому, что бизнес вышел за пределы местных географических границ, так что теперь предприятия могут сотрудничать с партнерами в других регионах или странах. Это делает данное исследование жизненно важным инструментом для ассоциаций национальных и международных организаций, которые рассматривают возможность сотрудничества при разработке и реализации таких стратегий и политики. Основной целью данного исследования является изучение структурных факторов, которые стимулируют или препятствуют сотрудничеству между организациями, а также стратегий, которые могут быть использованы для повышения эффективности кооперативных сетей, с особым акцентом на исходные позиции сотрудничества и их динамику в процессах в сложных сетях. В этом исследовании использовалось агентное моделирование и симуляция игр «Дилемма заключенного» и «Охота на оленя» в сложных сетях, представляющих африканские торговые отношения. Сети, использованные в моделировании, включали синтетические топологии (Клейнберга, Эрдёша-Реньи, Барабаши-Альберт) и эмпирическую сеть, основанную на реальных торговых связях между африканскими странами. Полученные результаты свидетельствуют о том, что исходное соотношение кооператоров и топология сети существенно повлияли на эволюцию кооперации и общую эффективность сети. Например, более высокая начальная доля кооператоров приводила к более высокой итоговой доле кооперации и более высокому среднему выигрышу на узел, причем динамика этих значений на сети африканских торговых отношений существенно отличается от таковой на синтетических сетях.
Ключевые слова: региональное/государственное партнерство, модели сотрудничества, дилемма заключенного, платежная матрица, комплексные сети, топологии, динамика сотрудничества.
