Game theory сonsiders human conflicts and cooperation in competitive situations. It includes at least two participants/players who by assumption should be rational and derive a certain gain/loss in the different outcomes that result due to the occurrence of the game. A potential of game theory in the building and analysis of behavioral models could be successfully utilized to address logistics and fleet management problems.

## Game theory in brief

Game theory could be described as a theoretical framework to describe various situations among competing players and facilitate optimal decision-making. Game in game theory is essentially a model of an interactive situation among rationally-behaving participants (players). It proved to be a productive approach in various fields, including economics, politics, business, and biology.

Game theory includes the following main parts:

- Player: a particular strategic decision-maker within the game.
- Strategy: a planned set of actions that players will perform, depending on particular circumstances.
- Game: a range of circumstances, that has a result depending on the player’s actions.
- Information set: represents the information, available at a given point in the game.
- Equilibrium: the moment in a game, in which players already made their decisions and outcome is reached.
- Payoff: forms a payout that a player receives from arriving at a particular outcome.

The game theory itself has various types such as simultaneous, sequential, symmetric, asymmetric, cooperative, and non-cooperative. We will not go deep into it here, as our purpose is just to give an idea of what game theory is and how it could benefit ti logistics and fleet management.

To provide an example of a game theory approach, let’s follow an example, given in [Geçkil, Anderson, 2010]. An example considers two players in a simple game. Player I has two options, choosing X or choosing Y; Player II has the same two options as well, X and Y. Let us assume they decide their moves simultaneously. If player I picks X and player II picks Y, a player I gets $10; player II gets $5. If player I picks Y and player II picks X, a player I gets $5; player II gets $10. If both pick X, a player I get $2, and player II get $8. Finally, if both pick Y, each gets $3.

Such games in game theory normally could be described using the so-called payoff matrix. Another powerful tool to illustrate and analyze games is a tree diagram. Both representations for the above-mentioned example are shown in the figure below.

## Game theory, logistics and routing

Let us consider a relatively simple example of how game theory could address routing and associated problems [N. Nisan, 2007]. Let’s assume that two traffic streams originate at proxy node O, and need to be routed to the rest of the network, as shown in the figure below.

Assume that node O is connected to the rest of the network through connection points A and B, where A is a little closer than B. However, both connection points get easily congested, therefore sending both streams via the same connection point would result in an extra delay. Favorable outcomes in this game would be for the two players to “coordinate” and send their traffic through different connection points.

This example shows that game theory could successfully address some of the routing problems, which are a crucial part of effective logistics and fleet management. Vehicle routing, in general, is a challenging task. We went through some aspects of vehicle routing in our post. Route optimization helps to quickly find the most optimal and convenient sequence for visiting each client and therefore forms an important feature of any innovation-driven modern telematics platform.

Navixy platform utilizes smart algorithms combined with advanced features of constraint programming and multi-purpose meta-heuristic techniques to account for everyday fleet management needs and addressing vehicle routing in a highly efficient and customer-beneficial way.

Applying game theory in fleet management and supply chain logistics potentially may lead to a better economic rationalization of these chains, reduced costs, improved resources management, and more insightful vehicle routing.

## References

- https://www.navixy.com
- https://www.investopedia.com/terms/g/gametheory.asp
- https://opsession.wordpress.com/2017/08/12/game-theory-application-to-supply-chain-management
- Z. Zhiwen et al, Supply Chain Logistics Information Collaboration Strategy Based on Evolutionary Game Theory, 2020.
- N. Nisan, Algorithmic Game Theory, 2007.
- M.J. Osborne, An Introduction to Game Theory, 2020.
- D. Simchi-Levi et al, The Logistics of Logistics, 2014.
- I.K. Geçkil and P.L. Anderson, Applied game theory and strategic behavior, 2010.
- A. Rzeczycki, Game theory in creating a supply chain logistics strategy – the possibility of applying a holistic approach, 2019.