A bit more about deal evaluation and contract evaluation

main.tex

@@ -69,7 +69,7 @@
 \date{\today} % Leave empty to omit a date
 \renewcommand{\maketitlehookd}{%
 \begin{abstract}
-\noindent Agorata is an implementation of the idealized economic agent, or, specifically, an aggregator of smart contracts. It combines one or more contracts proposed by the members of the network in a deal which can be evaluated as profitable for Agorata with low risks. Using this approach, Agorata can provide infrastructure for loans, flashloans, bets, derivatives, bridging between chaiNs, and many more financial instruments.
+\noindent Agorata is an implementation of the idealized economic agent, or, specifically, an aggregator of smart contracts. It combines one or more contracts proposed by the members of the network in a deal which can be evaluated as profitable for Agorata with low risks. Using this approach, Agorata can provide infrastructure for loans, flashloans, bets, derivatives, bridging between chains, and many more financial instruments.
 \end{abstract}
 }
 
@@ -124,6 +124,7 @@ Each action (message) has parameters $\theta$, including:
 The parameter space for each action can be constrained --- the smart contract can reject some of the messages. For instance, this can lead to the entire space consisting of a single element (the contract rejects everything except for one specific message, e.g. a specific person sending a specific amount of tokens).
 
 The main parameters of the state are the financial outcomes for the smart contracts.
+The state is written as a function of all parameters of all actions in a formal language.
 
 
 \subsection{Agent parameters}
@@ -139,13 +140,22 @@ Given these parameters, the value function $V((x_{i}), (t_{i}))$ (or $V(S)$) can
 The agent considers the worst case of the deal from the perspective of game theory: the best (from the perspective of the value function) actions of the agent and the ``worst'' actions of the counteragents.
 This sequence of events is the run through the value function in order to make a decision.
 
-Thus, a deal is considered profitable for the agent ($A$) $\iff$ $p(S_{i}) > 0$ $\iff$
+Thus, a deal is considered profitable for the agent ($A$) $\iff$ $p(S_{i})$ $\iff$
 $$V(S_{i})>0 \vee \\ (\forall a_{ij} (V(S_{ij}) > 0 \vee a.s = A) \wedge a_{ij}: V(S_{ij})>0)$$
 
+The algorithm starts at the node $S_{0}$, then considers all the possible actions (including the abscence of one) and calls the algorithm at $S_{0i}$. If there is any action of the counteragent that makes the contract non-profitable for the agent, the deal is considered non-profitable. If there is no possible action and the state includes profit for the agent, the deal is considered acceptable.
+
+\subsection{Example}
 
 
 \section{Contract evaluation algorithm}
 
+In the previous section of the article we specified how the decisions are made. One of the most important parts of the process is finding out whether there exists any action that makes the deal profitable or unprofitable. It is also important to know which actions the agent should make to maximize its output. How do we do that?
+
+The state parameters are represented as functions of action parameters expressed in a formal language.
+
+% Here it's about the path consideration algo + formal maximization + *template matching*
+
 \section{Applications}
 
 \subsection{Flashloans}