  Strategic interactions between competitive entities are generally considered
from the perspective of complete revelation of benefits achieved from those
interactions, in the form of public payoff functions and/or beliefs, in the
announced games. However, there exist strategic interplays between competitors
where the players have a choice to strategise under the availability of private
payoffs, in similar competitive settings. In this contribution, we propose a
formal framework for a competitive ecosystem where each player is permitted to
defect from publicly optimal strategies under certain private payoffs greater
than announced payoffs, given that these defections have certain acceptable
bounds in the long run as agreed by all players. We call this game theoretic
construction an Intention Game. We formally define an Intention Game, and
notions of participational equilibria that exist in such interactions that
permit public defections. We compare Intention Games with conventional
strategic form games, and demonstrate a type-theoretic construction of
Intention Games. In a partially honest setting, we give Intention Game
instances of a Cournot competition, secure interactions between mobile
applications, an Internet services' data sourcing competition between Internet
service providers through content delivery networks, and a Bitcoin mining
competition. We give a use of Intention Games to determine player participation
in a cryptographic protocol. Finally, we demonstrate the possibility of a dual
model of the Intention Games framework.
