Dynamic Competition Hypothesis

Dynamic Competition Hypothesis: competition networks, detecting alliances and leaders.

Abstract: introduce the dynamic competition hypothesis ,and explain it is main factors and concepts ,and validate the hypothesis by applying centrality measures on the data related to the dynamic competition networks, the manipulated data was extracted from a television show survivor which is an example of competitive networks.

Introduction:

In the early 80s the study on dynamic competition has been began ,which at first was belong to strategic management field, studying the behaviors of attacks and counterattacks between the companies ,as they proposed the behavior of competition between companies can lead to conclude a competitive strategy.

Chinese scholars start to introduce the methods and conclusions of dynamic competition in the late 90s,where at western literature it was generally known as dynamic competition.

At present dynamic competition hypothesis is evolve dynamically over time and can be hold more broadly and applied in many life fields as :marketing ,economics ,networking ,judicature, community ,and social networks.

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In this paper we are going to cover a dynamic competition theory applied in real world networks to discover and detecting alliances and leaders , in real world networks social games are good, simple, and easy example to validate the competition hypothesis by considering a players as nodes and the interaction between them as edges ,more precisely in the television show survivor which is a social game an edge is represented by voting the players which they represent the nodes against each other and here the competition hypotheses is works as a predictive tool to find out the leaders and alliances by record and studying the interaction (edges) between players (nodes).

Furthermore we are going to validate the competition hypothesis by a recording data from a social game we have did between our colleges in our university .

Dynamic Competition Hypothesis:

The competition behavior understood as interactive competitive action and response CITATION Zha14 l 1033 (Zhang & Gao , 2014), it can be considered as a forth and back cycle of attacks and counterattacks.

The key factors of dynamic competition :

• Competitive Interaction:
• Competitors And Competitive Action:

Competitors means the one who starts the competition, it is the attacker , and the attack action decision is influenced by the characteristics of the competitor ,the researches finds the general organization characteristics that affected in competitor action which they are : awareness ,motivation, capability. Awareness means the environment the competitor works or live in and how much the competitor realize the results of taken actions ,motivation is related to the feeling of loss or gain ,take actions depend on the expected benefits or do not take actions because of the possible loss, capability is the ability of a competitor to manage, organize, and execute his actions.

Competitive action is the most important concept of dynamic competition hypothesis ,its characteristics as following:

1. Competitive impact: taken actions against to a competitor actions.
2. Attract intensity: the degree of affected action on a competitor .
3. Implementation requirement: the effort level to implement the required action.
4. Type of action: tactical or strategic.

We can call the four previous points a competitive action traits.

3 Competitive Response: when the initiator competitor attack , the competitors will response to the attack(competitive action).competitive response has a characteristics which they are :number of response which clearly means the number of competitive response caused by competitors ,and response lag which means the time needed to a competitive action execution by a defender (competitor who attacked by initiator competitor).

• Competitive Interaction Result:

the final result after going through a competition interaction which is affected by a competitive action and competitive response .

• Dynamic Competition Networks

Networks are various and common in the real world or technological world ,in social networks either on the real world or on the technological world ,nodes are represent the agents , people ,or members , and edges are represent the social interaction between them ,for example a friendship or hostility ,for clarification in the technological world in Facebook agents are the users and edges are the friendships ,while in Twitter users are the agents and edges are the followings.

Focusing In the real world social networks dynamic competition hypothesis is used as a predictive tool to discover leaders and alliances , in a competition network nodes represent agents ,if the nodes u and v in a competition with each other we say there is a directed edge between them. A dynamic competition network is a competition network where directed edges are added over discrete time-steps CITATION Bon l 1033 (Bonato, Eikmeier, Gleich, & Malik).Dynamic competition network can have multiple edges ,and the nodes can be not joined by edges as in case of tournaments .

Dynamic competition networks need some graph theoretic terminology to manipulates and extract the data we need to represent the edges between nodes, so we use the standard metrics, such as in and out degree ,closeness , betweenness, and common out neighbors as key metric.

In the common out neighbor (CON) ,nodes u and v have a CON w if there is a directed edge between (u,w) and (v,w) ,to find the numbers of CON for a pair of nodes(u,v) we define:

CITATION Bon l 1033 (Bonato, Eikmeier, Gleich, & Malik) ?al games like a television sho will applied in a social games like a television sho by edges as in case of or on the technolog

For a strongly connected diagraph of a competition network and a node v ,define the closeness of u by:

CITATION Bon l 1033 (Bonato, Eikmeier, Gleich, & Malik)

Where d(u,v) denote the measured distance by one way.

The betweenness of a node v is defined by :

CITATION Bon l 1033 (Bonato, Eikmeier, Gleich, & Malik)

where ?xy(v) is the number of shortest one-way, directed paths between x and y that go through v, and ?xy is the number of shortest one-way, oriented paths between x and y. Both closeness and betweenness are well-studied centrality measures for complex networks CITATION Bon l 1033 (Bonato, Eikmeier, Gleich, & Malik).

To help determine the alliances and leaders in dynamic competitive networks arising in social network we need to apply network science ,dynamic competition hypothesis state that dynamic competition network arising from social networks assure the following four properties .

1. Alliances are near independent sets.
2. Strong alliances have low edge density.
3. Members of an alliance with high CON scores are more likely leaders.
4. Leaders exhibit high closeness, high CON scores, low in-degree, and high out-degree.

CITATION

Bon l 1033 (Bonato, Eikmeier, Gleich, & Malik) Alliances are group of agents support or drive a side or person to achieve mutual goals.in the social game show survivor group of players voting against one player to exclude him are called alliances because they have the same goal which is the same person they want to exclude, strong alliances will not vote against each other ,leaders are the agents with high standard metrics and their emitted edges can have a strong impact on the other agents edges. In survivor leaders are the winners or players who have a high standard metrics and affect the game development.

Survivor Data supported by the hypothesis

Survivor is an American television show in which the players called survivors, they are placed in a separated island coming from different cities and they must provide themselves food and shelter with limited support from the outside world, survivors are divided into tribes they live and work together, the tribes compete with each other to win the immunity ,the losing tribe had to have a tribal council where one of the members will exclusion.

at some point, the tribes will merge and they will continue to compete for their own immunity. survivors exclusion will become part of the jury when there are 3 or 2 survivors the jury will vote for one of them to become the sole survivor.

The main goal now is to validate the dynamic competition hypothesis using the data extracted from survivor manipulated by network science tools . Data was taken from Survivor Wiki , which contains information on contestants, their voting records and tribes, and catalogues of alliances. For computing centrality metrics and for the dynamic competition graph visualization, we used the open source Gephi software . CITATION Bon l 1033 (Bonato, Eikmeier, Gleich, & Malik)4.1 Borneo

Borneo was the first season of survivor the table is filled with the data recorded after all the votes between players are recorded ,and it analyzes the network statistics, ID refers to in-degree which represent the number of votes against the player ,OD refers to out-degree which represent the number of votes the player gave against other players, C refers to closeness, CON refers to common out neighbor score, and B refer to betweenness.

CON C B OD ID tribe name

42 0.737 28.7 10 6 Tagi Richard

34 0.682 0 12 0 Tagi Kelly

45 0.778 36.483 11 8 Tagi Rudy

44 0.778 16.467 10 7 Tagi Susan

38 0.7 17.917 9 9 Tagi Sean

29 0.636 33.067 8 7 Pagong Colleen

31 0.636 8.583 7 6 Pagong Gervaise

27 0.583 27.85 6 11 Pagong Jenna

15 0.412 4.833 5 6 Pagong Greg

17 0.56 7.233 4 4 Pagong Gretchen

17 0.412 1 3 4 Pagong Joel

12 0.5 1.317 3 4 Tagi Dirk

10 0.412 17.733 2 6 Pagong Ramona

4 0.452 1.733 2 6 Tagi Stacey

5 0.298 0.333 1 6 Pagong B.B

4 0.452 0.75 1 4 Tagi Sonja

We can notice that the players are entered in the table according to their elimination from the game , so that the first player entered is a winner, Richard which is the winner has one of the most highest closeness and CON scores, and because of Kelly was voted against Rudy and Susan when she won the immunity she played a role in Richard 's won even though Rudy and Susan have high scores .

5 supported data from our colleges game

Simply we are going to use in-degree and out-degree to estimate the leaders , alliances ,and the winner. the following table summarize the data.

OD ID Team Name

1 0 one Mai

1 0 one Noura

1 3 two Areeb

1 1 one Aysha

2 1 two Ibtehal

1 3 two Samia

2 1 one Najah

2 1 two Hala

the players are entered in the table according to their elimination from the game , so that the first player entered is the winner, low in-degree correspond to leaders so we can notice that Mai and Noura can be assumed leaders .

*the bold arrow means that they voted twice

Conclusion

the dynamic competition hypothesis is very important hypothesis to understand and analyze the competition behavior of competition in many life aspects ,it is also serves as a predictive tool to predict success , failure , action responses ,and many things depending on the case or the field .

Bibliography

1. Bonato, A. (2017, December 22). Survivor: Mathematical predictions of the big win. Retrieved from theconversation:
2. Bonato, A., Eikmeier, N., Gleich, D., & Malik, R. (n.d.). Dynamic Competition Networks: detecting alliances and leaders. Retrieved from
3. Zhang, J., & Gao , D. (2014). Review on the Research of Dynamic Competition Theory. Human Resource and Sustainability Studies. Retrieved from