And the first users play against the equilibrium strategies. Let us see whether you can beat the crowd:. Below is a gtreeWebPlay app that allows you to play a round of Kuhn Poker. The deck has only three cards: Jack , Queen and Ace and two players who each get one card after they both put one dollar into the blind. Below is an embedded app that allows you to play it against a randomly chosen earlier player:.
A game theoretic analysis of Kuhn poker using gtree can be found in this tutorial. A law and coding challenge I don't think it's a good idea The dbmisc package may help a bit. I'd like the gamble to earn money by fighting climate change. Game theory in R with the new gtree package 04 Sep Man pages Any scripts or data that you put into this service are public. R Package Documentation rdrr. We want your feedback! Note that we can't provide technical support on individual packages.
You should contact the package authors for that. Tweet to rdrrHQ. GitHub issue tracker. Personal blog. Our point is to show how various concepts from evolutionary game theory can be computed via the package EvolutionaryGames and where to find the conceptual, technical and mathematical details. In other words, we would like to stress that this little document is by no means intended to serve as an introduction to the fascinating field of evolutionary game theory itself.
Again, for the latter the reader is referred to the the two books by Weibull Weibull and Sandholm Sandholm For an in-depth mathematical discussion we also recommend the book by Hofbauer and Sigmund Hofbauer and Sigmund The package EvolutionaryGames focusses on single-population games with two, three or four phenotypes. The first author hopes to address multi-population games in a separate package based on EvolutionaryGames in the future. Smith and Price The function ESS. R receives three input arguments:.
It is well known that there are games which do not possess an ESS. A classical example is the game Rock-Scissors-Paper. In such a case our function ESS. R will return NULL. The concept of evolutionarily stable sets was first discussed by B.
Thomas in Thomas A very readable introduction can also be found in the book by Weibull Weibull , section 2. Note that any evolutionary stable strategy ESS constitutes an evolutionarily stable set and that the union of evolutionarily stable sets is again an evolutionarily stable set.
See the book by Weibull Weibull , section 2. Evolutionarily stable sets are not easy to compute and to plot. The package EvolutionaryGames computes evolutionarily stable sets of a game with two players and three strategies in the case that the game has an evolutionary stable strategy ESS.
If the two player three strategy game has no ESS, then the code returns a message stating that our algorithm cannot calculate evolutionarily stable sets for models that do not have a proper ESS.
The authors are very well aware that there are games having evolutionarily stable sets but no proper ESS. Still, as our package is not devoted to finding all symmetric Nash equilibria of a game and as there currently is no package for this task on CRAN, we decided only to handle the case of games with two players and three strategies possessing at least one proper ESS.
Within our algorithm, we need a proper ESS as a starting point for our computations. The authors feel that the possibility of computing and drawing evolutionarily stable sets in such cases is precious for teaching and research purposes.
However, note that computing and drawing evolutionarily stable sets is time consuming and is clearly the most elaborate task currently performed by the package EvolutionaryGames.
The basic game-theoretic model of biological natural selection is the replicator dynamic Taylor and Jonker Still, various alternative dynamics have been proposed and investigated for different applications.
Our package currently focusses on continuous dynamics only. The following itemization states which evolutionary dynamics are currently available in our package EvolutionaryGames:. Drawing phase diagrams for single-population games with two, three or four phenotypes with different dynamics is the main feature of the package EvolutionaryGames. Using phaseDiagram2S. R we obtain a phase diagram for the population share of hawks invading a population of doves under the replicator dynamics.
For similar phase diagrams, see e. In the phase diagrams for the three strategies the user may specify the following parameters for phaseDiagram3S. In the following we see three plots of the game Rock-Scissors-Paper under the Replicator dynamics with the same initial state:.
Finally, there is also the function phaseDiagram4S. R for the case of a symmetric matrix game with four strategies. Its parameters are rather similar to those of phaseDiagram3S.
Instead, there is an additional logical value noRGL handling diagram rotation. Finally, we present an example using the Smith dynamic. EvolutionaryGames offers you to create your own dynamics. In particular, it is easy to write your own continuous dynamics. First of all, a dynamic is nothing other than a function that is passed as a parameter to the corresponding function for creating phase diagrams. The following code fragment shows you the minimum necessary structure of an arbitrary dynamic:.
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