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Game-theory insights into asymmetric multi-agent games

As artificial intelligence systems begin to have an increasing part in the actual world it is critical to comprehend how varying systems will have interactions with each other. 

In one of the newer research papers, put out in the journal Scientific Reports, a branch of game theory is leveraged to illuminate this issue. Specifically, it is examined how two intelligent systems behave and react to a specific type of scenario referred to as asymmetric game, which consists of Leduc Poker and several board games like Scotland Yard. Asymmetric games also naturally model specific real-word situations like automated actions where buyers and sellers function with differing motivations. The outcomes provide us fresh insights into these scenarios and unveil a shockingly simplistic fashion to analyse them. While the research is around how this theory is applicable to the interaction of several artificial intelligence systems, the belief is that outcomes could also hold good in economics, evolutionary biology, and empirical game theory among others. 

Game theory is a domain of mathematics that is leveraged to undertake analysis of the techniques leveraged by decision makers in competitive scenarios. It can be applicable to humans, animals, and computers in several scenarios but is usually leveraged in AI research to study “multi-agent” settings where there is in excess of one system, for instance various household robots collaborating to clean the home. Conventionally, the evolutionary dynamics of multi-agent frameworks have been analysed leveraging simplistic, symmetric games like the classic Prisoner’s Dilemma, where every player has access to a similar set of behaviours. Even though these games can furnish useful insights into how multi-agent systems function and inform us how to accomplish a desirable result for all players – referred to as the Nash equilibrium – they cannot model every scenario. 

Our new strategies facilitates us to swiftly and simply identify the techniques leveraged to identify the Nash equilibrium in more complicated asymmetric games – characterised as games where every player has differing techniques, objectives, and rewards. These games – and the new strategy we leverage to comprehend them can be demonstrated leveraging an instance from ‘Battle of the Sexes’ a coordination game typically leveraged in game theory research. 

In this, two players have to coordinate a night out to either the movies or to the opera. One of the players has a slight leaning towards the opera and one of them has a bit of a preference for the movies. The game is asymmetric as while both players have access to similar options, the correlating rewards for each one are differing on the basis of the player’s preferences. To maintain their conducive relationship, or equilibrium, the players must opt for the same activity. (Therefore, the zero payoff for differing activities) 

This game has a trio of equilibria: i) both players making a decision to go to the opera, ii) both making a decision to go to the movies, and iii) a final, combined option, where each individual player will choose their preferred option 3/5ths of the time. This final option, which is stated to be ‘unstable’ can be swiftly uncovered leveraging our strategy through simplification – or decomposing the asymmetric game into its symmetric counterparts. These counterpart games basically considers the reward table of every player as an independent symmetric two-player game with equilibrium points that overlap with the original asymmetric game. 

In the plot displayed below, the Nash equilibrium is plotted for the dual, simple counterparts facilitating us to swiftly identify the optimum technique in the asymmetrical game (a). The reverse can also be performed, leveraging the asymmetrical game to identify the equilibrium in its symmetrical counterparts. 

This strategy can also be applied to other games, which includes Leduc Poker, which is described in detail in the paper. In all of these scenarios, the strategy proves to be mathematically simplistic, enabling a swift and straightforward analysis of asymmetric games. The hope is that it will facilitate our comprehension of several dynamic systems, which includes multi-agent environments. 

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