Is There a Point of Equilibrium in a Game with No Winners?

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SUMMARY

The discussion centers on the existence of equilibrium points in games with no winners, specifically referencing game theory concepts. Participants agree that such equilibria can exist, exemplified by a game where players incur a cost initially but receive no returns thereafter. The conversation highlights the relevance of Nash Equilibrium, a fundamental concept in game theory introduced by John Nash, which describes a situation where no player can benefit by changing their strategy while others keep theirs unchanged.

PREREQUISITES
  • Understanding of game theory principles, particularly Nash Equilibrium.
  • Familiarity with mathematical functions and their derivatives, such as dU(p1,...pk)=0.
  • Basic knowledge of probability theory as it relates to game outcomes.
  • Concept of strategic decision-making in competitive environments.
NEXT STEPS
  • Research Nash Equilibrium and its applications in various strategic scenarios.
  • Explore the implications of zero-sum games in game theory.
  • Study calculus applications in game theory, focusing on optimization techniques.
  • Investigate examples of games with no winners and their equilibrium states.
USEFUL FOR

Game theorists, mathematicians, economists, and anyone interested in strategic decision-making in competitive environments will benefit from this discussion.

eljose
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A game with no winners...

let,s use some of game theory...let,s suppose we have a game played by n players with k parameters given by the function U(p1,p2,...pk) so we get that there exist a point of equilibrium dU(p1,...pk)=0 so nobody wins could exist that equilibrium...(my question is if there is an state of equilibrium in a game in which nobody wins)...
 
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Well, it's hard to understand you but the answer appears to be

1. of course there are (eg agame that costs 1 dollar to play on the first turn and is free afterwards and where all players obtain 0 dollars with probability 1 on every turn for one of an infinite number of examples).

2. what has this got to do with calculus and analysis?
 
When I read this I immediately had to think of Nash's contribution to the Game Theory, with his Nash Equilibrium. Perhaps this or this helps...
 

Thread 'How does this derivative work? And why the speed of light remains?'

Relativistic Momentum, Mass, and Energy Momentum and mass (...), the classic equations for conserving momentum and energy are not adequate for the analysis of high-speed collisions. (...) The momentum of a particle moving with velocity ##v## is given by $$p=\cfrac{mv}{\sqrt{1-(v^2/c^2)}}\qquad{R-10}$$ ENERGY In relativistic mechanics, as in classic mechanics, the net force on a particle is equal to the time rate of change of the momentum of the particle. Considering one-dimensional...
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