The process of making a professional video game is a complex task that involves people from many backgrounds to join together and work on something creative. We can examine the ways game theory is used to help make decisions when designing the gameplay as high level decision trees can be made to model the flow and pathways and use payoff matrices to model skill or level change.
There are many methods for design approaches which include flowcharts, storyboards, topological maps, UML and decision trees. Decision trees can be used to model gameplay where different paths in the decision tree relate to different paths that can be chosen by the player or the different outcomes that can arise from the actions of the player. A decision tree is a branching tree style diagram that can show the set of possible actions and decisions that can be made by the player. It can overall model the way the player moves through all the possibilities of the game.
When creating decision trees it is based on the main game interactions of most interest. We can use fixed inanimate objects that will be represented as boxes in the decision tree. The tree will show the likelihood of events occuring, for example for a coin toss game it would show the likelihood of getting heads or tails. In more complex games it would show the probability of getting a success. It would seem too large and out of scale to make a decision tree for the whole game and so instead we can break it into segments or per mission.
The figure represents the design of a simple example of a very small segment of a hypothetical game scenario. It shows the game objects with which the player may interact on how fast and how accurately opponents 1 and 2 will respond.
A payoff matrix can be used to model the player’s decision making the process into a grid structure in order to analyze,document and communicate the skill or challenge levels within the parts of the game. One axis will represent the player’s decision and the other axis of the payoff matrix will represent the opponent’s decisions. It is unfeasible to have a payoff matrix for every possible decision in the game however it’s practical to make one model more generic level decisions made by players given in segments of a game. For example in the video game pong, the accuracy of the movements made by the player affects the game. This is because the ball’s contact with the ping-pong rectangle (bat) returned the ball at smaller angles which made it harder to hit the next time. A payoff matrix can model high and low player accuracy outcomes as generic player decisions. For multiplayer games, statistical analysis of the strategies used by a large number of players via payoff matrices can be used to understand the strategies of the players which will inform us more about the game design. This ultimately can help balance different elements in the game.
Table 1 shows a payoff matrix that could be proposed by a game designer to determine what skill level would be required regarded to the gameplay involving either of the two software-based opponents from Figure 1. In terms of skill level, the matrices could be used to apply Nash equilibrium.
Table 2 shows a payoff matrix based upon an analysis of different games played during playtesting for a given section of a video game. The first number in each cell is the payoff (or probability of success) to the opponent and the second number is the success probability for the player. If they use the same strategy, then the player will win 50% of the time. However if the player chooses a high accuracy/low speed strategy and the opponent chooses a high speed/low accuracy strategy, the player will win 80% of the time. Overall high level payoff matrices can help design the skill and challenge level for different sections of the game.
References
https://journals-sagepub-com.myaccess.library.utoronto.ca/doi/pdf/10.1177/1555412017740497
It’s interesting how game theory can apply to a video games balance depending on different player strategies. However, I feel like even if such hypothetical payoff matrices can be seen for certain game scenarios, the game developers usually never use them in order to balance the game design. These payoff matrices can simply just be there, where one strategy gives one player a very high chance of winning and gives the other player a very low chance to win no matter what he does. For example, for League of Legends, reworked Pantheon had a 100% ban rate at worlds 2019 for high impactful reasons such as that he could be flexed top, mid, jungle, and support, and that he could easily dive turrets with his team and tank tower shots due to his E ability. If this were a hypothetical payoff matrix, the team who first picks Pantheon would probably have a 90% chance of winning no matter what the opposing team picks in their draft, so the only viable strategy for the second pick team to ban it. It’s game theory matrices such as this where I don’t think game balance can ever truly be balanced since there are so many possible scenarios that would need to be taken into consideration.
It’s actually a good idea to make game theory a part of the design of something, conflicts always occur during the manufacture of mathematical model just like the video game you have described,
it requires many high level and advanced technologies from different fields, the relations between each of them is complex which gives the producer challenges to maintain the equilibrium. Game theory provides prefect, balanced strategies to help maintain the equilibrium.